Respuesta :
Using a system of equations, it is found that Susan had 44 quarters, 11 dimes and 27 nickels.
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We are going to use:
- x as the number of quarters.
- y as the number of dimes.
- z as the number of nickels.
A quarter is worth $0.25. A dime is worth $0.1, and a nickel is worth $0.05. Total of $13.45, then:
[tex]0.25x + 0.1y + 0.05z = 13.45[/tex]
4 times as many quarters as dimes, thus:
[tex]x = 4y \rightarrow y = 0.25x[/tex]
16 less dimes than nickels, thus:
[tex]z = y + 16 = 0.25x + 16[/tex]
Replacing in the first equation, we find x:
[tex]0.25x + 0.1y + 0.05z = 13.45[/tex]
[tex]0.25x + 0.1(0.25x) + 0.05(0.25x + 16) = 13.45[/tex]
[tex]0.2875x = 12.65[/tex]
[tex]x = \frac{12.65}{0.2875}[/tex]
[tex]x = 44[/tex]
Now, with x, we find y and z:
[tex]y = 0.25x = 0.25(44) = 11[/tex]
[tex]z = y + 16 = 11 + 16 = 27[/tex]
Susan had 44 quarters, 11 dimes and 27 nickels.
A similar problem is given at https://brainly.com/question/24342899
