Mathematics: Suppose you have x quarters, 3x + 2 dimes, 5x +1 nickels, and 6x + 4 pennies. the value of the coins is $4.59. write an equation that represents this situation, and find how many of each coin you have. show your work.

Suppose you have x quarters, 3x + 2 dimes, 5x +1

Ответ:

mxlx27

12.03.2022

$\text{Suppose you have x quarters, (3x+2) dimes, (5x+1) nickels and (6x+4) pennies}\\
\text{and total value of the coins is }\$ 4.59\\
\\
\text{we know that the value of 1 quarter is}=\$ 0.25\\
\\
\text{value of 1 dime}=\$0.10\\
\\
\text{value of 1 Nickel}=\$ 0.05\\
\\
\text{value of 1 Penny}=\$ 0.01\\
\\
\text{so the equation that represents the given situation is}$

0.25 x+0.10(3x+2)+0.05(5x+1)+0.01(6x+4)=4.59

$\\
\text{now to find the number of each coin, we solve it. so}\\
\\
0.25 x+0.3x+0.20+0.25x+0.05+0.06x+0.04=4.59\\
\\
0.86x+0.29=4.59\\
\\
\Rightarrow 0.86x=4.59-0.29\\
\\
\Rightarrow 0.86x=4.3\\
\\
\Rightarrow x=\frac{4.3}{0.86}\\
\\
\Rightarrow x=5$

So the number of quarters is: 5

Number of dimes=3x+2=3(5)+2=17

Number of nickels=5x+1=5(5)+1=26

And number of Pennies=6x+4=6(5)+4=34

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Suppose you have x quarters, 3x + 2 dimes, 5x +1 nickels, and 6x + 4 pennies. the value of the coins is $4.59. write an equation that represents this situation, and find how many of each coin you have. show your work.

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