Answer:
14 Dimes and 56 Quarters
Explanation:
Let D and Q stand for the numbers of Dimes(D) and Quarters(Q). Also, I'll use pennies (not dollars) to eliminate the hassle of decimal points.
We are told that:
10D + 25Q = 1540 [Kendra has $15.40 in dimes and quarters]
We also find that:
Q = 4D [4 times as many quarters as dimes]
Substitute the expression for Q in the second equation into the first:
10D + 25Q = 1540
10D + 25(4D) = 1540
10D + 100D = 1540
110D = 1540
D = 14
Since Q = 4D:
Q = 4(14)
Q = 56
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Check:
Does 10D + 25Q = 1540 ?
10(14) + 25(56) = 1540
140 + 1400 = 1540 YES
Does Q = 4D ?
56 = 4(14) YES