# 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 Aug 28, 2016 #### Answer: $\frac{31}{49}$#### Explanation: $3 \times x + 64 = 7 \times x$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 $3 \times x$and $7 \times x$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 $- 4 \times \frac{x}{-} 4 = - \frac{64}{-} 4$this gives $$x = 16  $3 \times 16 = 48$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 $\frac{62}{98}$divide by two (2) gives 31: 49 for the new ratio. Aug 28, 2016 #### Answer: $31 : 49$#### 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 Aug 30, 2016 #### Answer: $\text{Maya : Sophia "->" } 31 : 49$#### 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: $\left(\text{Maya")/("Sophia}\right) \to \frac{3}{7}$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#