# The ratio of Maya's money to Sophia is 3 : 7. Sophia has $64 more than Maya. If Sophia gives 14 of her money to Maya, what will be the new ratio?

##### 3 Answers

#### Explanation:

If you add 64 to Maya's money it will be equal to Sophia's money.

as the ratio is 3: 7 whatever amount of money ( x) is in the ratio of the

3x + 64 = 7x Subtract 64 from each side of the equation

3x + 64 - 64 = 7 x - 64 this gives

3x = 7 x -64 Subtract 7x from both sides of the equation

3x - 7x = 7x - 7x - 64 this gives

-4x = -64 divide both sides by -4

```
x = 16
```

# 7 xx 16 = 112 for Sophia

Add 14 to Maya and subtract 14 from Sophia

48 + 14 = 62 for Maya

112 - 14 = 98 for Sophia

The new ratio is

31: 49 for the new ratio.

#### Explanation:

There is a difference of 4 parts between 3 parts and 7 parts.

The amounts differ by $64.

If 4 parts is 64, 1 part is 16.

The amounts of money are therefore

M : S

3 : 7

48 : 112

Sophia gives $14 to Maya:

62 : 98

31 : 49

#### Explanation:

With ratio you are comparing counts of a whole.

The ration of 3:7 means that the total count is 3+7=10

Showing the ratio in fractional format:

The difference in the amount of money at the start is $64. So

7 parts - 3 parts = 4 parts and the difference is $64

So 1 part is

'.............................................................

Check:

'.......................................................

Sophia gives $14