Library / CEMC Gauss (Grade 8) /455 of 525

CEMC Gauss (Grade 8), 2024

Algebra Difficulty 2.8 Junior Find the answer Canada

The ratio of the number of quarters (worth $\$0.25$ each) to the number of dimes
(worth $\$0.10$ each) to the number
of nickels (worth $\$0.05$ each) in a
jar is $9:3:2$ . If the total value of
the quarters and dimes is $\$17.85$ ,
what is the total value of the nickels?

Pick one

Solution

The ratio of the number of quarters to the number of dimes to the
number of nickels is $9:3:2$ .

This means that for some positive integer $k$ , the number of quarters is $9k$ , the number of dimes is $3k$ , and the number of nickels is $2k$ .

The value of each quarter is $\$0.25$
or $25$ cents, and so the value of
the quarters in the jar, in cents, is $25\times9k=225k$ .

The value of each dime is $\$0.10$ or
$10$ cents, and so the value of the
dimes in the jar, in cents, is $10\times3k=30k$ .

The total value of the quarters and dimes is $\$17.85$ or $1785$ cents, and so $225k+30k=1785$ or $255k=1785$ , and so $k=\frac{1785}{255}=7$ .

The number of nickels is $2k=14$ , and
so the value of the nickels is $\$0.05\times14=\$0.70$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.