Question 1200308: If Qasim has 4 times as many quarters as nickels and they have a combined value of 735 cents, how many of each coin does he have? Found 3 solutions by Theo, josgarithmetic, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 25 * x + 5 * y = 735
x is the number of quarters; each quarter is worth 25 cents.
y is the number of nickels; each nickel is worth 5 cents.
you are given that x = 4 * y (4 times as many quarters as nickels)
your two equations are:
25 * x + 5 * y = 735
x = 4 * y
in the first equation, replace x with 4 * y to get:
25 * 4 * y + 5 * y = 735
simplify to get:
100 * y + 5 * y = 735
combine like terms to get:
105 * y = 735
solve for y to get:
y = 735 / 105 = 7
since x = 4 * y, then x = 28
25 * x becomes 25 * 28 = 700
5 * y becomes 5 * 7 = 35
25 * x + 5 * y becomes 700 + 35 = 735 cents.
solution is 28 quarters and 7 nickels.
You can put this solution on YOUR website! .
If Qasim has 4 times as many quarters as nickels and they have a combined value
of 735 cents, how many of each coin does he have?
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Let x be the number of nickels.
Then the number of quarters is 4x.
Write the total money equation
25 *(4x) + 5x = 735 cents.
Simplify and find x
100x + 5x = 735
105x = 735
x = 735/105 = 7.
ANSWER. 7 nickels and 7*4 = 28 quarters.
Solved.
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It can be solved mentally (the same solution as above, only re-told in wording form).
Group coins in the sets in a way that each group consists of 1 nickel and 4 quarters.
According to the problem, such grouping is possible.
Each group is worth 4*25 + 5 = 105 cents.
The number of group is 735/105 = 7.
It gives the answer above.
Solved in two ways, for your better understanding.
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