Question

Harry had $32. He spent all the money buying three notebooks for x dollars each and four packs of index cards for y dollars each. If Harry had bought five notebooks and five packs of index cards, he would have run short by $18. Use the system of equations to solve for x and y:

3x + 4y = 32
5x + 5y = 50
a. x = 8, y = 2
b. x = 1, y = 5
c. x = 2, y = 8
d. x = 5, y = 1

Answer 1

To solve this system of equations, we can use the method of substitution or elimination. Using the substitution method, we find that x = 8 and y = 2.

So, the correct answer is A)

Step-by-step explanation:

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the substitution method.

We'll solve the first equation, 3x + 4y = 32, for x:

x = (32 - 4y) / 3

Substitute this expression for x in the second equation, 5x + 5y = 50:

5((32 - 4y) / 3) + 5y = 50

Simplify and solve for y:

160 - 20y + 15y = 150

-5y = -10

y = 2

Now substitute the value of y back into the first equation to find x:

3x + 4(2) = 32

3x + 8 = 32

3x = 24

x = 8

Therefore, x = 8 and y = 2.

So, the correct answer is A) x = 8, y = 2.