# Answer to Question #16086 in Algebra for lena safi

Question #16086

matt has $4.45 in dimes and nickels. If he has 52 coins, how many dimes and nickels does he have?

Expert's answer

Let Matt has d dimes and n nickels. Then we've got a system of linear equations:

10d + 5n = 445& (1)

d + n = 52& (2)

Let's solve it.

(2) ==> d = 52 - n

(1): 10(52 - n) + 5n = 445, or

520 - 10n + 5n = 445, or

- 5n = -75 ==> n = 15,

and

d = 52 - 15 = 37.

So, matt has 37 dimes and 15 nickels.

10d + 5n = 445& (1)

d + n = 52& (2)

Let's solve it.

(2) ==> d = 52 - n

(1): 10(52 - n) + 5n = 445, or

520 - 10n + 5n = 445, or

- 5n = -75 ==> n = 15,

and

d = 52 - 15 = 37.

So, matt has 37 dimes and 15 nickels.

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