# Money related Word problems.

#### bergausstein

##### Active member
A wallet has $\$460$, in$\$5$, $\$10$, and$\$20$ bills. the number of $\$5$bills exceeds twice the number of$\$10$ bills by $4$, while the number of $\$20$bills is 6 fewer than the number of$\$10$ bills. how many bills of each type are there?

i solved this problem in two ways by 1st choosing the unknown represent the number of $\$10$bills and 2nd by choosing the unknown represent the number of$\$20$ bills.

and i got these answers from my two methods, $14$ $\$10$bills,$8\$20$ bills and $32$ $\$5$bills. on my third method i chose the unknown represent the number of$\$5$ bills.
and here how it goes,

let $x=$ number of $\$5$bills,$\frac{x}{2}-4=$number of$\$10$ bills
$\frac{x}{2}-4-6=$ number of $\$20$bills$5x+10\left(\frac{x}{2}-4\right)+20\left(\frac{x}{2}-10\right)=4605x+5x-40+10x-200=46020x-240=46020x=700$then,$x=35$---> from here the number of$\$5$ bill is bigger than my previous result. can you pinpoint where is the mistake here? thanks!

p.s use only one variable.

#### MarkFL

Staff member
If $x$ is the number of \$5 bills then: $$\displaystyle \frac{x-4}{2}$$ is the number of \$10 bills.

$$\displaystyle \frac{x-16}{2}$$ is the number of \$20 bills. #### bergausstein ##### Active member If$x$is the number of \$5 bills then:

$$\displaystyle \frac{x-4}{2}$$ is the number of \$10 bills. $$\displaystyle \frac{x-16}{2}$$ is the number of \$20 bills.
if i use that $x=32$ which is the number of $\$5$bill. thanks! if some question why did you divide$x-4$by$2$? in my first method what the number of$\$5$ bill is $2x+4$
that's why i thought of taking the opposite operation so i came up with $\frac{x}{2}-4$.

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#### MarkFL

If $x$ is the number of \$5 bills and$y$is the number of \$10 bills, then we have:
$$\displaystyle x=2y+4\implies y=\frac{x-4}{2}$$
I think you might have solved this problem already, but just for practice can you show how to get the number of \$20 bills in terms of$x$? MarkFL showed how to get the number of \$10 bills but didn't show all the steps as to how he got $\dfrac{x-16}{2}$ for the number of \\$20 bills. Can you show how to get this value?