Question

Question 3 of 8, Step 1 of 2 2/10 Correct Consider the following word problem: Sarah has some dimes and quarters. If she has 29 coins worth a total of $4.40, how many of each type of coin does she have? Step 1 of 2: Use the variables d and a to set up two equations to solve the given problem.

Answer 1

Answer:

The number of dime coins is 19

The number of quarters coins is 10

Explanations:

1 Dime = $0.10

1 quarter = $0.25

Let the number of dime coins be represented by d

Let the number of quarter coins be represented as a

If the total amount of coins she has equals $4.40

This can be interpreted mathematically as:

0.10 d + 0.25 a = 4.40

Multiply the above equation throgh by 100

10d + 25a = 440....................(1)

Since the total number of coins she has equals 29.

The mathematical interpretation of this is:

d + a = 29..................(2)

To solve the equation, make "a" the subject of the formula in equation (2)

a = 29 - d...............(3)

Substitute equation (3) into equation (1)

10d + 25(29 - d) = 440

10d + 725 - 25d = 440

25d - 10d = 725 - 440

15d = 285

d = 285/15

d = 19

Substitute the values of "d" into equation (3)

a = 29 - 19

a = 10

The number of dime coins is 19

The number of quarters coins is 10