please answer all 3 questions

Question

Bryce and Mauricio each building birdhouses for the park beautification project. Bryce can build 2 birdhouses per week and has already built 12 houses. Mauricio can build 3 birdhouses per week and has already built 8 houses. In how many weeks will they built the same number of houses? How many houses will that be? If they each need to build 24 houses, who will finish first?

Answer 1

12 + 2w = 8 + 3w

Solve for w.

Total = 12 + 2w + 8 + 3w

12 + 2w = 24, solve for w

8 + 3w = 24, solve for w

Which w is less?

Answer 2

Bryce has built 12 birdhouses and can build 2 more per week. If he has to build 24 birdhouses total, then:

12 + 2w = 24

2w = 12

w = 6 so it will take Bryce 6 weeks.

Mauricio has built 8 birdhouses and can build 3 more per week. If he has to build 24 birdhouses total, then:

8 + 3w = 24

3w =16

w = 16/3 = 5 and 1/3 so it will take Mauricio 5 and 1/3 weeks.

Therefore we know that Mauricio will finish first.

Now let’s find out in how many weeks they will have built the same number of birdhouses.

12 + 2w = 8 + 3w

12 = 8 + w

4 = w so in four weeks they will have built the same number of birdhouses. How many birdhouses will that be?

12 + 2(4) = 12 + 8 = 20 and

8 + 3(4) = 8 + 12 = 20

So we know the answer is 20 birdhouses.

Hope that helps! Please contact me if you’d like to arrange for tutoring. I explain things patiently and step by step and will go over it as many times as you need to understand it. Karen