Answer:
3 : 1
Step-by-step explanation:
The ratio of coins is ...
1 2/5 : 2 1/3 = 7/5 : 7/3 = 3 : 5
The quarters have 5 times the dollar value of nickels, so the ratio of dollar values is ...
5(3) : 5 = 3 : 1
The quarters have 3 times the dollar value of the nickels.
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Additional comment
The number of nickels is 5/3 times the number of quarters, so is 5/3(24) = 40.
The dollar value of the quarters is 24($0.25) = $6.
The dollar value of the nickels is 40($0.05) = $2.
As above, the ratio of dollar values is 6:2 = 3 : 1.
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There are a few different ways to compute the ratio of fractions. The one we used here may be a little unusual. All are equivalent.
[tex]\bullet\quad\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}\qquad\text{"invert and multiply"}\\\\\bullet\quad\dfrac{a}{b}\div\dfrac{c}{b}=\dfrac{a}{c}\qquad\text{ratio of numerators with the same denominator}\\\\\bullet\quad\dfrac{a}{b}\div\dfrac{a}{c}=\dfrac{c}{b}\qquad\text{inverse ratio of denominators with the same numerator}[/tex]
