Question

Devi and her brother had the same amount of money. After Devi spent 2/5 of her money and her brother spent 3/10 on his money, they had 78$ left

altogether. How much money did they spend altogether?

Answer 1

Let us assume Devi or her brother amount = $x.

Devi spent 2/5 of x, that is 2/5 x.

Remaining amount of Devi = x- 2/5 x = 5x/5 - 2x/5 = 3x/5.

Her brother spent 3/10 of x, that is 3/10 x.

Remaining amount of her brother = x- 3/10 x = 10x/10 - 3x/10 = 7x/10.

Total amount they left together = $78.

Therefore,
`3x/5\:+\:7x/10\:=\:78\:`

`(3x)/(5)+(7x)/(10)=78`

`\mathrm{Find\:Least\:Common\:Multiplier\:of\:}5,\:10:\quad 10`

Multiply equation by LCM 10.

`(3x)/(5)\cdot \:10+(7x)/(10)\cdot \:10=78\cdot \:10`

`6x+7x=780`

`13x=780`

`\mathrm{Divide\:both\:sides\:by\:}13`

`(13x)/(13)=(780)/(13)`

`x=60`

Therefore, each one spent $60 and they spent altogether = 60+60 = $120.