Question

There is a jar containing 80 all of which are either quarters or die the total value of the coins is $13 how many of each coin are there in the jar make sure to write the Quetion social work

Answer 1

Answer:

There are 33 quarters and 47 dimes

Step-by-step explanation:

Let the number of quarters be q.

Let the number of dimes be d.

There are 80 coins in total. Therefore:

q + d = 80 ________(1)

The total value of coins is $13.

The value of a quarter is $0.25 and the value of a dime is $0.10. This means that:

0.25q + 0.10d = 13 _____(2)

We have a system of equations:

q + d = 80 ________(1)

0.25q + 0.10d = 13 ____(2)

From (1):

q = 80 - d

Put this in (2):

0.25(80 - d) + 0.10d = 13

20 - 0.25d + 0.10d = 13

Collecting like terms:

-0.15d = 13 - 20

-0.15d = -7

d = -7 / -0.15

d ≅ 47

Therefore:

q = 80 - 47 = 33

There are 33 quarters and 47 dimes.