Colin and Shaina wish to buy a gift for a friend. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have? A. 5 B. 10 C. 20 D. 23 E. 36

Tolnaio

Tolnaio

Answered question

2021-01-22

Colin and Shaina wish to buy a gift for a friend. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have?
A. 5
B. 10
C. 20
D. 23
E. 36

Answer & Explanation

Alannej

Alannej

Skilled2021-01-23Added 104 answers

Let q be the number of quarters, d be the number of dimes, and n be the number of nickels that they have.
Since they have $4.00 in coins, then 0.25q+0.1d+0.05n=4.
Since they have 35 coins in all, then q+d+n=35.
Since the number of quarters they have is half the number of nickels, then q=12n.
Substitute q=12n=0.5n into the first two equations and then simplify:
0.25q+0.1d+0.05n=4 q+d+n=35
0.25(0.5n)+0.1d+0.05n=4 0.5n+d+n=35
0.125n+0.1d+0.05n=4 d+1.5n=35
0.1d+0.175n=4
Solving d+1.5n=35 for dd gives d=35−1.5n. Substitute this into 0.1d+0.175n=4 and solve for n:
0.1d+0.175n=4
0.1(35−1.5n)+0.175n=4
3.5−0.15n+0.175n=4
3.5+0.025n=4
0.025n=0.5
n=20
They then have 20 nickels so they have q=12n=12(20)=10 quarters. The correct answer is then B. 10. ​ ​ ​ ​ ​ ​

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