Question

A collection of 22 dimes and quarters has a total value of $4.00. Write a system of equations that defines this situation and solve using any method.

Answer 1

To solve this problem, create a system of equations using the given information and solve using any method.

Step-by-step explanation:

To solve this problem, we can create a system of equations using the given information. Let's say the number of dimes is represented by 'd' and the number of quarters is represented by 'q'. Since there are a total of 22 coins, we have the equation:

d + q = 22

Now, since the total value of all the coins is $4.00, we can create another equation using their respective values:

0.10d + 0.25q = 4.00

Now we can solve this system of equations using any method such as substitution or elimination.

Answer 2

Since dimes + quarters = 22
And dimes are 0.10 cents as quarters = 0.25 cents
Let’s make d = dime, q = quarter
d + q = 22
0.10d + 0.25q = 4.00
Let’s use substitution
d + q = 22, get d or q by itself
d = 22 - q (plug into second equation)
0.10(22-q) + 0.25q = 4
2.2 - 0.10q + 0.25q = 4
2.2 + 0.15q = 4
0.15q = 1.8, q = 12
Since there are 12 quarters you know there are 10 dimes (22 in total)

Solution: 10 dimes, 12 quarters