Sarah and the gift boxes.

Question

Sarah prepared 10 gift boxes for a class party. She packed x gift boxes

of magnets and y gift boxes of keychains. A gift box of magnets weighed

2 pounds while a gift box of keychains weighed 3 pounds. The total weight

of all the gift boxes was 24 pounds.

a) Write a system of two linear equations.

b) State with reasons whether the system of equations has a unique

solution, is inconsistent, or dependent.

c) How many gift boxes of magnets did Sarah pack?

Answer 1

Your systems are

Equation 1 for the number of boxes

x + y =10

Equation 2 for the weight

2x + 3y = 24

You can solve by Elimination or Substitution.

I will use Elimination below

If you multiply Equation 1 by negative 2 you can eliminate x and solve for y

Equation 1 multiplied by negative becomes

-2x - 2y = -20

Combine the above with Equation 2 to eliminate x

-2x - 2y = -20

2x + 3y = 24

Leaves

y = 4

Substitute this y back into the original Equation 1 to find x

x + y = 10

With the y value becomes

x + 4 = 10

Subtract 4 from both sides to solve for x

x = 6

x = 6 Boxes of magnets

y = 4 Boxes of Key Chains

I'll leave it to you to review the equations and numbers to answer b

Give it a try.

Answer 2

x = number of magnet gift boxes

y = number of keychain gift boxes

10 = total number of gift boxes

x + y = 10

x 2 lb magnet gift boxes + y 3 lb keychain gift boxes = 24 lbs

2x + 3y = 24

multiply first equation by 2

2x + 2y = 20

same x but different y so the system of equation has a unique solution.

subtract equations:

2x + 3y = 24

- (2x + 2y = 20)

y = 4 keychain gifts

since 10 gifts, x = 6 magnet gifts