Question

Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?

Answer 1

1) When this does happen, how many posters will each Avenger have completed?

24 posters each.

2) If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?

y = 12 + 6x.......... Equation 1

y = 12x .......... Equation 2

Explanation:

1) When this does happen, how many posters will each Avenger have completed?

We are told in the question:

Number of days = x

Number of posters = y

Ms. Ironperson has completed 12 posters and will complete 6 more per day.

y = 12 + 6x.......... Equation 1

Mr. Thoro has not started yet but can make 12 per day.

y = 12x................Equation 2

Hence, the equations needed to solve this problem:

y = 12 + 6x.......... Equation 1

y = 12x .......... Equation 2

We substitute 12x for y in equation 1

y = 12 + 6x.......... Equation 1

12x = 12 + 6x

Collect like terms

12x - 6x = 12

6x = 12

x = 12/6

x = 2

Hence, since x = the number of days,

The number of days = 2 days

Substitute 2 for x in Equation 2

y = 12x .......... Equation 2

y = 12 × 2

y = 24 posters.

Since y = number of posters,

number of posters = 24 posters.

We were told in the question that, when Mr Thoro catches up with Ms Ironperson, that would both have completed the same number of posters.

Hence, both Avengers would have completed 12 posters each.