Question

A collection of nickels dimes and quarters is worth 3.00. The ratio of nickels to dimes to quarters is 3:2:1. How many quarters are it the collection

Answer 1

Answer:

5 quarters

Explanation:

From the information we were given, we can develop the following equations:

Let "nickel" be represented by "n", "dimes" by "d" & "quarters" by "q"

A collection of nickels dimes and quarters is worth 3.00. Mathematically represented as:

$n+d+q=3.00$

We are given the ratio of nickels to dimes to quarters is 3:2:1. The equation above becomes:

$\begin{gathered} 3(0.05)+2(0.10)+1(0.25)=3.00 \\ (0.15+0.20+0.25)x=3 \\ 0.60x=3.00 \\ \text{Divide both sides by ''0.60'', we have:} \\ x=\frac{3}{0.60}=5 \\ x=5 \\ \text{Multiplying the ratios, we have:} \\ nickels=3\times5=15 \\ dimes=2\times5=10 \\ quarters=1\times5=5 \end{gathered}$

Therefore, there are 5 quarters in the collection