Question

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?

Answer 1

`31/49`

Explanation:

`3 xx x + 64 = 7 xx x`

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 `3 xx x` and `7 xx x` so take the equation and solve for x

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

`-4 xx x/-4 = -64/-4` this gives

x  =  16

`3 xx 16 = 48` for Maya

# 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 `62/98` divide by two (2) gives

31: 49 for the new ratio.

Answer 2

`31 : 49`

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

Answer 3

`"Maya : Sophia "->" "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:

`("Maya")/("Sophia") -> 3/7`

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 `($64)/4 = $16`

`("Maya")/("Sophia")" " ->" " 3/7" " ->" " (3xx$16)/(7xx$16) = ($48)/($112)`

'.............................................................
Check: `10" units"xx$16= 160`

`$48+$112 = $160`
'.......................................................

Sophia gives $14

`("Maya")/("Sophia")" "->" "($48+$14)/($112-$14)" "->" "($62)/($98)`

`("Maya")/("Sophia")" "->" "31/49`