Student Manual
Bridge to College Mathematics, Unit 5. Lesson 4
BRIDGE COLLEGE
Task #14: Boomerangs
Phil and Cath make and sell boomerangs for a school event. The money they raise will go to charity.
They plan to make them in two sizes small and large.
• Phil will carve them from wood. The small boomerang takes two hours to carve and the large one
takes three hours to carve. Phil has a total of 24 hours available for carving.
• Cath will decorate them. She only has time to decorate 10 boomerangs of either size.
• The small boomerang will make $8 for charity. The large boomerang will make $10 for charity.
They want to make as much money for charity as they can. How many small and large boomerangs
should they make? How much money will they then make?

Step 1; It takes Phil 2 hours to carve a small boomerang and 3 hours to carve a large one. He has 24 hours to carve however many boomerangs he can. Cath can decorate 10 boomerangs. Assume x to be the number of small boomerangs and y to be the number of large boomerangs. So the following equation can be formulated using the given information

Equation 1. 2x + 3y = 24 hours (2 hours to make each x and 3 hours to make each y)

Equation 2. x + y = 10 (Cath can only decorate 10 boomerangs)

From equation 2, y = 10 - x, take this as equation 3.

Step 2; Substituting equation 3 in equation 1 we get

2x + 3y = 2x + 3(10 - x) = 24, 2x + 30 -3x = 24, -1x = -6, so x = 6

Substitute x = 6 in equation 2 so

x + y = 6 + y = 10, so y =4

So they should make 6 small boomerangs and 4 large boomerangs.

Step 3; Now we calculate the money they will make. Each small boomerang will make $8 and each large one will make $10. So

6 × 8 / each small boomerang + 4 × 10 / each large boomerang

=(6 × 8)+ (4 × 10) = 48 + 40 = $88.

heavenwilkins11 heavenwilkins11 · Answer 2 · 2020-12-02T23:08:42+01:00

heavenwilkins11 heavenwilkins11

02-12-2020

Answer:

88 dollas

Step-by-step explanation:

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