word problem

[user948123]

How to solve: Karen's dad gave her money for Christmas. Her mom gave her twice as much money as her dad and her little brother gave her half as much money as her dad gave her. If the total amount of money that Karen received for Christmas was $105, how much money did Karen receive from her brother?

 

[soroban]

Hello, user948123!

This is the only one that needs some Algebra.

Karen's dad gave her money for Christmas.
Her mom gave her twice as much money as her dad.
Her brother gave her half as much money as her dad gave her.
If the total amount of money that Karen received for Christmas was $105,
how much money did Karen receive from her brother?

\(\displaystyle \text{Let }x\text{ = amount her father gave her.}\)

\(\displaystyle \text{Then }2x\text{ = amount her mother gave her.}\)

\(\displaystyle \text{And: }\tfrac{1}{2}x\text{ = amount her brother gave her.}\)


\(\displaystyle \text{The total is \$105: }\;x + 2x + \tfrac{1}{2}x \;=\;105\)

. . . . . \(\displaystyle \tfrac{7}{2}x \:=\:105 \quad\Rightarrow\quad x \:=\:30\)


\(\displaystyle \text{Therefore: }\;\begin{Bmatrix}\text{Father:} &x & =& \$30 \\ \text{Mother:} &2x & =& \$60 \\ \text{Brother:} &\frac{1}{2}x & =& \$15 \end{Bmatrix}\)