**High School Number Sense Lesson 99: Percent Greater Than**

This concept appeared

**4 times**this year, with a median placement at

**question # 24**.

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**Number Dojo Level: 165**

There are a couple of different variations of this problem:

- A is ___% more than B
- If A is X% more than B, and B is Y% more than C, then A is ___% more than C

**How to Solve Variation # 1:**

- Subtract: A - B
- Divide this result by B
- Convert to a percent

**Example 1: 64 is what % more than 40? ___%**

- Subtract: 64 - 40 =
**24** - Divide: 24 ÷ 40 =
**3/5** - Convert to a percent: 3/5 = .6 =
**60**%

**Example 2: 24 is what percent more than 18? ___%**

- Subtract: 24 - 18 =
**6** - Divide: 6 ÷ 18 =
**1/3** - 1/3 =
**33 1/3**%

**Example 3: 54 is what percent more than 40? ___%**

- Subtract: 54 - 40 =
**14** - Divide: 14/40 =
**7/20** - 7/20 =
**35**%

**Example 4: 32 is what percent more than 28? ___%**

- Subtract: 32 - 28 =
**4** - Divide: 4 ÷ 28 =
**1/7** - 1/7 =
**14 2/7**%

**How to Solve Variation # 2:**

- Convert each % to the equivalent decimal
- Multiply the decimal together
- Subtract 1
- Convert to a percent

**Example 5: If A is 30% more than B, and B is 30% more than C, then A is ___% more than C**

- If A is 30% more than B, A is
**1.3**times B - If B is 30% more than C, B is
**1.3**times C - 1.3 x 1.3 =
**1.69** - 1.69 - 1 =
**.69** - The answer is
**69**%

**Example 6: If A is 20% more than B and B is 15% more than C, then A is ___% more than C**

- A is
**1.2**times B, and B is**1.15**times C - 1.2 x 1.15 = (1 + .2) x 1.15 = 1.15 + .23 =
**1.38** - 1.38 - 1 =
**.38**=**38**%

**Example 7: If P is 10% greater than Q and Q is 20% greater than R, then P is what % greater than R? ___%**

- P is
**1.1**times Q, and Q is**1.2**times R - 1.1 x 1.2 =
**1.32** - 1.32 - 1 =
**.32**=**32**%

**Example 8: If A is 20% more than B and B is 10% less than C, then A is ___% more than C**

- Be careful here...B is
**less than**C - A is
**1.2**times B, and B is**0.9**times C - 1.2 x 0.9 =
**1.08** - 1.08 - 1 =
**.08**=**8**%

**Up Next for High School: DivFrac1000**