AMC10 2004 B

AMC10 2004 B · Q15

AMC10 2004 B · Q15. It mainly tests Systems of equations, Money / coins.

Patty has 20 coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have 70 cents more. How much are her coins worth?

Patty 有20枚硬币，包括镍币和10美分币。如果她的镍币变成10美分币，而10美分币变成镍币，她将多70美分。她的硬币总值多少？

(A) $1.15 $1.15

(B) $1.20 $1.20

(D) $1.30 $1.30

(E) $1.35 $1.35

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Because the value of Patty’s money would increase if the dimes and nickels were interchanged, she must have more nickels than dimes. Interchanging one nickel for a dime increases the amount by 5 cents, so she has $70/5=14$ more nickels than dimes. Therefore she has $$\frac{1}{2}(20-14)=3$$ dimes and $20-3=17$ nickels, and her coins are worth $3\cdot 10+17\cdot 5=115$ cents $=\$1.15$.

（A）因为如果把一角硬币和五分硬币互换，Patty 的钱会增加，所以她的五分硬币一定比一角硬币多。用一枚五分换成一枚一角会使金额增加 5 美分，因此她的五分硬币比一角硬币多 $70/5=14$ 枚。所以她有 $$\frac{1}{2}(20-14)=3$$ 枚一角硬币，以及 $20-3=17$ 枚五分硬币。她的硬币总价值为 $3\cdot 10+17\cdot 5=115$ 美分 $=\$1.15$。

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