A Vending Machine Contained $13 In Dimes And Quarters. There Were 70 Coins. How Many Dimes Does It Have?
February 18th, 2010 Posted in Información General
A)A vending machine contained $13 in dimes and quarters. There were 70 coins. How many dimes did the vending machine contain?
B)How many quarters did the machine contain if the 70 coins were valued at $10.75?
Please. Tell me how to do it, don’t just leave the answer i want the steps clearly.
February 18th, 2010 at 11:39 pm
Hi,
D + Q = 70
10D + 25Q = 1300
Multiply the first equation by -10 and add the equations together.
-10(D + Q = 70)
10D + 25Q = 1300
-10D - 10Q = -700
10D + 25Q = 1300
—————————
15Q = 600
Q = 40
There were 40 quarters, so there were 70 - 40 or 30 dimes. < ==ANSWER
If the coins were valued at $10.75, then:
D + Q = 70
10D + 25Q = 1075
Multiply the first equation by -10 and add the equations together.
-10(D + Q = 70)
10D + 25Q = 1075
-10D - 10Q = -700
10D + 25Q = 1075
—————————
15Q = 375
Q = 25
There were 25 quarters, so there were 70 - 25 or 45 dimes. <==ANSWER
I hope that helps!!
February 18th, 2010 at 11:39 pm
Let d be the number of dimes and q the number of quarters
then
d + q = 70
Using the amounts
0.10 * d + 0.25 * q = 13.00
Multiply the second equation by 100 to clear the decimals
10d + 25q = 1300
Multiply the first equation by 10
10d + 10q = 700
Subtract the second equation from the first
10d - 10d + 25q - 10q = 1300 - 700
15q = 600
Divide both sides by 15
15q/15 = q = 600/15 = 40
So there are 40 quarters and 30 dimes
February 18th, 2010 at 11:39 pm
(A). The number of dimes is “D”, and the number of quarters is “Q”.
10D + 25Q = 1300
D + Q = 70
Solve the pair of equations.
Multiply second equation by 10
10D + 10Q = 700
Subtract the equations
0 + 15Q = 1300 - 700 = 600
Divide by 15
Q = 40
Now it’s easy to see that:
D = 30.
February 18th, 2010 at 11:39 pm
A) 40 quarters ( 10 dollars) and 30 dimes (3 dollars)
B)I dont know