Knowee
Questions
Features
Study Tools

William and Aiden like to share stickers. If William gives 40 stickers to Aiden, the ratio of William to Aiden's stickers will be 1 : 7. If William gives 50 stickers to Aiden, their ratio will be 1 : 12. How many stickers does William have?

Question

William and Aiden like to share stickers. If William gives 40 stickers to Aiden, the ratio of William to Aiden's stickers will be 1 : 7. If William gives 50 stickers to Aiden, their ratio will be 1 : 12. How many stickers does William have?

🧐 Not the exact question you are looking for?Go ask a question

Solution 1

Let's denote the number of stickers William has as W and the number of stickers Aiden has as A.

From the problem, we have two equations based on the ratios given:

  1. If William gives 40 stickers to Aiden, the ratio of William to Aiden's stickers will be 1 : 7. This can be written as: (W - 40) / (A + 40) = 1 / 7.

  2. If William gives 50 stickers to Aiden, their ratio will be 1 : 12. This can be written as: (W - 50) / (A + 50) = 1 / 12.

Now we have a system of two equations, and we can solve it step by step.

First, let's multiply each equation by 7 and 12 respectively to get rid of the fractions:

  1. 7 * (W - 40) = A + 40
  2. 12 * (W - 50) = A + 50

This simplifies to:

  1. 7W - 280 = A + 40
  2. 12W - 600 = A + 50

Now, we can set the two equations equal to each other since they both equal A:

7W - 280 = 12W - 600

Solving for W, we get:

5W = 320

So, W = 64.

Therefore, William has 64 stickers.

This problem has been solved

Solution 2

Let's denote the number of stickers William has as W and the number of stickers Aiden has as A.

From the problem, we have two equations based on the ratios given:

  1. If William gives 40 stickers to Aiden, the ratio of William to Aiden's stickers will be 1 : 7. This can be written as: (W - 40) / (A + 40) = 1 / 7.

  2. If William gives 50 stickers to Aiden, their ratio will be 1 : 12. This can be written as: (W - 50) / (A + 50) = 1 / 12.

Now we have a system of two equations, and we can solve it step by step.

First, let's multiply each equation by its denominator to get rid of the fractions:

  1. 7 * (W - 40) = A + 40, which simplifies to 7W - 280 = A + 40.

  2. 12 * (W - 50) = A + 50, which simplifies to 12W - 600 = A + 50.

Now we have two new equations:

  1. 7W - A = 320
  2. 12W - A = 650

Subtract the first equation from the second:

(12W - 650) - (7W - 320) = 0

This simplifies to:

5W = 330

So, W = 330 / 5 = 66.

So, William has 66 stickers.

This problem has been solved

Similar Questions

Benjamin and Marus like to share stickers. If Benjamin gives 40 stickers to Marus, the ratio of Benjamin to Marus's stickers will be 1 : 5. If Benjamin gives 90 stickers to Marus, their ratio will be 1 : 9. How many stickers does Benjamin have?

Wilson and Jamie like to share stickers. If Wilson gives 10 stickers to Jamie, the ratio of Wilson to Jamie's stickers will be 1 : 8. If Wilson gives 70 stickers to Jamie, their ratio will be 1 : 11. How many stickers does Wilson have?

Lisa and Angeline like to share stickers. If Lisa gives 70 stickers to Angeline, the ratio of Lisa to Angeline's stickers will be 1 : 6. If Lisa gives 90 stickers to Angeline, their ratio will be 1 : 7. How many stickers does Lisa have?

The ratio of Ali's stickers to Bala's stickers is 3 : 7. After Bala gave 42 stickers to Ali, they had an equal number of stickers. How many stickers did Ali have at first?

Cheko and Keddy like to share stickers. If Cheko gives 30 stickers to Keddy, the ratio of Cheko to Keddy's stickers will be 1 : 7. If Cheko gives 40 stickers to Keddy, their ratio will be 1 : 11. How many stickers does Cheko have?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.