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You have a jar containing 74 coins, consisting entirely of pennies and quarters, worth a total of $6.74. How many quarters are in the jar? Type in your numerical answer only; do not type any words or letters with your answer.

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JeanaShupp

Answer:  25

Step-by-step explanation:

We know that , 1 dollar = 100 pennies

i.e. 1 penny = $ 0.01

1 dollar = 4 quarters

i.e. 1 quarter = $ 0.25

Let x be the number of pennies and y be the number of quarters in the jar, then the system of equation represents the given situation will be :-

[tex]x+y=74------(1)\\\\ 0.01x+0.25y=6.74------(2)[/tex]

Multiply 100 on both sides of equation (2), we get

[tex]x+25y=674-------(3)[/tex]

Subtract (1) from (3), we get

[tex]24y=600\\\\\Rightarrow\ y=\dfrac{600}{24}=25[/tex]

Substitute y= 25 in equation (1), we get

[tex]x+25=74\\\\\Rightarrow\ x=74-25=49[/tex]

Hence, there are 49 pennies and 25 quarters in the jar.

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