SOLUTION: Kendra has $13.20 in dimes and quarters. If she has 4 times as many quarters as dimes, how many of each coin does she have?
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Question 837607: Kendra has $13.20 in dimes and quarters. If she has 4 times as many quarters as dimes, how many of each coin does she have?
Found 2 solutions by mxgirl22, josh_jordan:
Answer by mxgirl22(39) (Show Source): You can put this solution on YOUR website!
Kendra has $13.20 in dimes and quarters. If she has 4 times as many quarters as dimes, how many of each coin does she have?
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1st.) Label variables
d=dimes
q=quarters
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2nd.) Get information from second sentence: 4 times as many quarters as dimes.
So:
q=4d
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3rd.) Make equation.
0.10d+(4d*0.25)=$13.20
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4th.) Solve for "d".
0.10d+(4d*0.25)=$13.20
0.10d+1d=$13.20
1.10d=$13.20
1.10d/1.10=$13.20/1.10
d=12
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5th.) Solve for "q". Use the equation we made in step 2 and plug in the value we got for "d" in step 4.
q=4d
q=4(12)
q=48
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6th) Check work, using values we got for "q" and "d".
0.10d+(0.25q)=$13.20
0.10(12)+[0.25(48)]=$13.20
0.10(12)+[12]=$13.20
0.10(12)+[12]=$13.20
1.20+[12]=$13.20
$13.20=$13.20
Checks!
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Kendra has 48 quarters and 12 dimes.
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To solve, we need to set this word problem up as a set of equations. We are told that Kendra has $13.20 in dimes and quarters. We know that a dime is = .10 and a quarter is equal to .25. So, our first equation would look like:
.10d + .25q = 13.20, where d=dimes and q=quarters
Next, we are told that the number of quarters is 4 times the number of dimes. In other words
q = 4d
Now, we can substitute 4d for q in equation 1:
.10d + .25(4d) = 13.20 ----->
.10d + 1d = 13.20 ----->
1.10d = 13.20
Now, we can divide both sides of this equation by 1.10:
d = 13.20/1.10 ----->
d = 12
Therefore, Kendra has 12 dimes. We know that the number of quarters is 4 times the number of dimes. So, 4 * 12 = 48. Hence, we have 48 quarters.
ANSWER: 12 dimes & 48 quarters
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