Question

Megan spent two out of five of her money on a doll and half of the remainder on a musical box she spent eight dollars more on the doll than on a musical box how much money did she have left

Answer 1

Answer:

Megan has left with $24.

Step-by-step explanation:

Let the total money she has be 'y'.

Given:

Megan spent two out of five of her money on a doll.

So we can say that;

Money spent on doll = $\frac{2}{5}y$

Also Given:

half of the remainder on a musical box.

Money spent on musical box = $(y-\frac{2}{5}y)\frac{1}2$

Now we will make the denominator common using LCM we get;

Money spent on musical box =$(\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}$

Now Given:

she spent eight dollars more on the doll than on a musical box.

$\frac{2y}{5} = \frac{3y}{10}+8$

Combining like terms we get;

$\frac{2y}{5}-\frac{3y}{10}=8$

Now we will make the denominator common using LCM we get;

$\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\ 80$

Money spent on doll = $\frac{2}{5}y=\frac{2}{5}\times 80 = \ 32$

she spent eight dollars more on the doll than on a musical box.

So we can say that;

Money spent on musical box = Money spent on doll -8 = $32-8 = \ 24$

Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.

framing in equation form we get;

remaining money left = $80-32-24= \ 24$

Hence Megan has left with $24.