experiment5491
Answered

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There are 102 coins with the value of 17.10$ and they are quarters and dimes, how many of the coins are dimes

Sagot :

alidemonahabib

Answer:

Let x = number of dimes

y = number of quarters

Equation 1 is then x + y = 100, that one is easy.

Now you have to worry about values of each, and since a dime is $0.10 and a quarter is $0.25, that means that the number of each times their respective dollar amounts has to add up to the total dollar amount.

Equation 2 is then 0.1x + 0.25y = 14.05

To rewrite for clarity you have:

x + y = 100 (1)

0.1x + 0.25y = 14.05 (2)

Now you can solve this any number of ways, I'm going to use addition by multiplying both sides of equation 1 by -1/10 and then adding it to equation 2.

-0.1x - 0.1y = -10

0.1x + 0.25y = 14.05

0.15y = 4.05

don't let the decimals trip you up, that's the same as

15y = 405

y = 27 quarters

Now use that value in the original equation 1 to get

x = 100 - 27 = 73 dimes

To check use the values in the equation 2

$0.1*(73) + $0.25*(27) = $14.05

$7.30 + $6.75 = $14.05

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