Question

Kendra has $15.40 in dimes and quarters. If she has 4 times as many quarters as dimes, how many of each coin

Answer 1

Answer:

14 Dimes and 56 Quarters

Step-by-step 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