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

$\frac{3x}{5}+\frac{7x}{10}=78$

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

Multiply equation by LCM 10.

$\frac{3x}{5}\cdot \:10+\frac{7x}{10}\cdot \:10=78\cdot \:10$

$6x+7x=780$

$13x=780$

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

$\frac{13x}{13}=\frac{780}{13}$

$x=60$

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