SOLUTION: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80. a) set up a sy

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Question 1141884: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80.
a) set up a system if equations to represent the situation.
b) find the number of quarters in the bank.
please give details, thankyou
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
6.90 = 690 cents.
q is the number of quarters
d is the number of dimes

you get two equations.

first equation is 25 * q + 10 * d = 690

this is because each quarter is worth 25 cents and each dime is worth 10 cents.

second equation is 10 * q + 25 * d = 780

this is because each quarter is worth 10 cents and each dime is worth 25 cents.

the number of quarters and dimes is the same.

what is changed is their value as stated in the problem statement.

your two equations that need to be solved simultaneously are:

25 * q + 10 * d = 690
10 * q + 25 * d = 780

multiply both sides of the second equation by 2.5 and leave the first equation as is to get:

25 * q + 10 * d = 690
25 * q + 62.5 * d = 1950

subtract the first equation from the second to get:

52.5 * d = 1260

solve for d to get d = 24

the first equation of 25 * q + 10 * d = 690 becomes 25 * q + 10 * 24 = 690

simplify to get 25 * q + 240 = 690

subtract 240 from both sides to get 25 * q = 450

solve for q to get q = 18

you have 18 quarters and 24 dimes.

if the value of the quarters is 25 cents and the value of the dimes is 10 cents, the total value is 25 * 18 + 10 * 24 = 690.

if the value of the quarters is 10 cents and the value of the dimes is 25 cents, the total value is 10 * 18 + 25 * 24 = 780.

the solution is confirmed to be good.

the solution is that the number of quarters is 18.








Answer by josgarithmetic(39620) About Me  (Show Source):