Math Problem Solved: Finding The Number When 170 Is 85 Percent

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Quick Answer

• To find the number when 170 is 85 percent, you divide 170 by 0.85.
• The answer you’ll get is 200.
• So, 170 is 85 percent of 200. Simple as that.

Who This Is For

• Students wrestling with basic algebra and percentage calculations, especially those facing word problems.
• Anyone who needs to quickly reverse a percentage calculation in real life, like figuring out the original price before a discount or the total amount before tax.
• Golfers trying to understand performance metrics. For example, if a player’s driving accuracy is 85% on a specific course and they hit 170 fairways, how many total drives did they take? This helps contextualize their performance against benchmarks.

What to Check First When Finding 170 is 85 Percent of What Number

• Identify the Parts: Make sure you clearly understand which number is the “part” and which is the “percent.” In this case, 170 is the “part” (the known portion), and 85 percent is the “percent” (the rate).
• Confirm the Goal: You’re looking for the “whole” number – the original total amount from which the part was taken. This is the unknown you need to solve for.
• Understand the Relationship: Verify that the percentage (85%) represents a fraction of the whole number you’re trying to find. This means the whole number must be larger than the part (170).
• Contextualize for Golfers: If you’re analyzing player stats, is 170 the number of successful putts, and 85% is their putting success rate? Or is it the number of fairways hit out of a total number of drives? Always clarify what the numbers represent to avoid misinterpreting performance trends.

Step-by-Step Plan: Finding The Number When 170 Is 85 Percent

This is a pretty standard percentage problem, like figuring out the original ticket price before a sale or understanding a player’s win percentage based on a certain number of victories. Let’s break it down.

• Action: Understand the problem statement thoroughly.
• What to look for: Read carefully to confirm that 170 is explicitly stated as being “85 percent of” some unknown total number. This tells you 170 is the “part” and 85% is the “percent.”
• Mistake to avoid: Don’t assume 170 is the “whole” number. The phrasing “170 is 85 percent of what number” clearly indicates 170 is the portion, not the total. For a golfer, this might be like seeing “170 birdies” and knowing that’s “85 percent of their total rounds played.” You’re not looking for the total number of rounds in 170; you’re looking for the total rounds that produced 170 birdies at an 85% rate.

• Action: Convert the percentage to its decimal form.
• What to look for: To use percentages in calculations, you need to convert them into decimals. Divide the percentage by 100. So, 85 percent becomes 85 / 100 = 0.85. This decimal represents the fractional value of the whole.
• Mistake to avoid: Using the percentage number (85) directly in your equation. This will lead to a wildly incorrect result because you’re essentially treating 85 as a multiplier instead of 0.85. It’s like trying to calculate a discount using 20 instead of 0.20 – you’d end up with a massive, nonsensical price.

• Action: Set up the fundamental percentage equation.
• What to look for: The basic formula relating part, percent, and whole is: Part = Percent × Whole. In our specific problem, substituting the knowns, this becomes: 170 = 0.85 × Whole. This equation clearly shows the relationship between the numbers.
• Mistake to avoid: Incorrectly assigning the values to “Part” or “Percent.” Always double-check which number represents the portion you know and which represents the rate. For a pro golfer, if they made 170 putts and that represents 85% of their total putts taken, then 170 is the Part and 0.85 is the Percent.

• Action: Isolate the “Whole” variable.
• What to look for: To find the “Whole,” you need to rearrange the equation. Since the “Whole” is currently being multiplied by 0.85, you’ll perform the inverse operation: division. Divide both sides of the equation by 0.85. This gives you: Whole = Part / Percent.
• Mistake to avoid: Multiplying when you should be dividing. This is a common slip-up. If you were to multiply 170 by 0.85, you’d get a number smaller than 170, which contradicts the fact that 170 is 85% of the whole. This would be like trying to find the original price by multiplying the sale price by the discount percentage, which makes no sense.

• Action: Perform the division calculation.
• What to look for: Now, simply plug the numbers into your rearranged equation: Whole = 170 / 0.85. Use a calculator to ensure accuracy.
• Mistake to avoid: Simple arithmetic errors. Even with the correct method, a misplaced decimal or a wrong digit during division will lead to the wrong answer. Always take a moment to double-check the numbers you’re entering into the calculator.

• Action: Verify your answer.
• What to look for: Once you have your result (which should be 200), plug it back into the original equation to see if it holds true. Does 85% of 200 equal 170? Calculate 0.85 × 200. If you get 170, you’ve nailed it.
• Mistake to avoid: Skipping this final check. It’s your best defense against calculation errors or a misunderstanding of the problem. If the numbers don’t match up, it’s back to step one to find where you went wrong.

Understanding 170 is 85 Percent of What Number in Context

This type of problem pops up everywhere, not just in math class. Think about a golfer’s performance:

• Driving Accuracy: If a pro golfer hits 170 fairways in a season, and that represents 85% of their total drives, how many drives did they take? We’re looking for the total number of drives (the “whole”). Using our formula: Whole = 170 / 0.85 = 200 drives. So, they took 200 drives and hit 170 of them in the fairway. This gives context to their 85% accuracy – it’s out of a significant number of attempts.

• Greens in Regulation (GIR): Suppose a player is aiming for 85% GIR and has hit 170 greens so far. How many rounds has this player played? Again, 170 is the “part,” and 0.85 is the “percent.” The “whole” would be the total number of rounds. Whole = 170 / 0.85 = 200 rounds. This tells us they’ve played 200 rounds and hit 170 greens, achieving their 85% goal.

• Birdie Conversion Rate: If a player records 170 birdies in a tournament series, and this is 85% of all the birdie opportunities they had, how many birdie opportunities were there in total? The calculation remains the same: Whole = 170 / 0.85 = 200 opportunities. This helps evaluate how effectively they capitalized on chances to score.

The key takeaway is that when you know a part and the percentage it represents, you can always find the original whole by dividing the part by the decimal form of the percentage. This is a fundamental skill for understanding stats, scores, and performance metrics in any field, including golf.

Common Mistakes When Finding 170 is 85 Percent of What Number

Making a few simple errors can send your answer way off. Let’s cover the usual suspects.

• Mistake: Using 85 instead of 0.85 in calculations.
• Why it matters: This is probably the most common mistake. Using 85 directly means you’re treating the percentage as a whole number multiplier, not a fraction. If you calculate 170 * 85, you get a massive number (14,450), which is clearly not the “whole” number that 170 is a part of. It completely distorts the relationship between the numbers.
• Fix: Always convert the percentage to a decimal by dividing by 100 before you use it in any calculation. 85% becomes 0.85. This ensures you’re working with the correct fractional value.

• Mistake: Incorrectly setting up the equation (e.g., multiplying when division is needed).
• Why it matters: The problem asks “170 is 85 percent of what number?” This means 170 is the result of multiplying the unknown whole number by 0.85. To find the unknown whole, you must reverse that multiplication with division. If you multiply 170 by 0.85, you’re calculating 85% of 170, which gives you a smaller number (144.5), not the original whole.
• Fix: Clearly identify what you are solving for. If you need to find the whole, and you know the part and the percent, the formula is always Whole = Part / Percent (decimal). Think of it like this: if you have a part and you know what fraction it is, you divide the part by that fraction to get the whole.

• Mistake: Calculation errors during division.
• Why it matters: Even if you have the right method and the correct numbers, a simple arithmetic slip-up can lead to the wrong final answer. For example, misplacing a decimal in 170 / 0.85 could result in 20 or 2000 instead of 200.
• Fix: Use a calculator for division. Double-check the numbers you enter. It’s also good practice to estimate your answer beforehand. Since 85% is close to 100%, the whole number should be slightly larger than 170. This quick check can flag a wildly incorrect calculation.

• Mistake: Confusing “part” and “whole” in the problem statement.
• Why it matters: If you mistakenly believe 170 is the total number of something, and 85% is just a characteristic of it, your entire approach will be flawed. The phrasing “170 is 85 percent of what number” is crucial. It tells you 170 is the subset, not the superset.
• Fix: Read the problem carefully, paying close attention to prepositions like “of” and “is.” “170 is 85 percent of X” means 170 = 0.85 X. If it said “What is 85 percent of 170?”, then you would multiply 0.85 170.

• Mistake: Not understanding how percentages relate to numbers greater than 100%.
• Why it matters: While not directly applicable to this specific problem (85% is less than 100%), it’s a common area of confusion. If a problem stated “255 is 85% of what number?”, the answer would be 300. But if it said “340 is 85% of what number?”, the answer would be 400. The principle remains the same: divide the part by the decimal.
• Fix: Remember that percentages over 100% mean the part is larger than the whole. For instance, if a player increased their scoring average by 15% from last year, and this year’s average is 170, last year’s average was 170 / 1.15, not 170 / 0.85.

FAQ

• How do I set up a word problem involving percentages like this one?
• First, identify the three key components: the “part” (a specific quantity or amount), the “percent” (the rate expressed as a percentage), and the “whole” (the total amount or original value). In the problem “170 is 85 percent of what number?”, 170 is the part, 85% is the percent, and you’re looking for the whole. The general formula is Part = Percent × Whole. To find the whole, you rearrange it to Whole = Part / Percent (with the percent converted to a decimal).

• What is the formula for finding the whole number when a part and percentage are known?
• The formula is: Whole = Part / Percent. Crucially, the “Percent” must be converted into its decimal form first. So, if you have a part and know it represents a certain percentage, divide that part by the decimal equivalent of the percentage to find the whole. For example, if 50 is 25% of a number, the whole is 50 / 0.25 = 200.

• Can I solve this problem (170 is 85 percent of what number) without a calculator?
• Yes, you can solve it without a calculator using long division. You would divide 170 by 0.85. This involves moving the decimal point two places to the right in both the divisor (0.85 becomes 85) and the dividend (170 becomes 17000), then performing the long division of 17000 by 85. While possible, using a calculator is significantly faster and reduces the chance of arithmetic errors.

• What if the percentage was greater than 100%? For example, if 200 is 120 percent of what number?
• The same principle applies. You convert the percentage to a decimal: 120% becomes 1.20. Then, you divide the part by the decimal: Whole = 200 / 1.20. In this case, the whole number would be approximately 166.67. Notice that when the percentage is over 100%, the “part” (200) is larger than the “whole” (166.67), which makes sense.

• How does this concept apply to golf statistics like player rankings or performance metrics?
• Understanding this calculation is vital for interpreting player stats. For instance, if a golfer is ranked 170th out of 200 players in a certain category (like driving distance), you can calculate their percentile rank. Their rank is 170 out of 200. To find what percentage of players are better than them, you’d calculate (200 – 170) / 200 = 30 / 200 = 0.15, or 15%. This means they are in the top 15% of players for that metric. Conversely, if you know a player has a 75% success rate on putts inside 10 feet, and they made 170 such putts, you can find the total number of attempts: 170 / 0.75 = 226.67 attempts. This gives context to their performance.