A boy has 380 prize tickets he wants to exchange for action figures at a prize booth. At this prize booth 5 tickets can be exchanged for a large action figure, and 7 tickets can be exchanged for 2 small action figures. The boy wants 4 times as many small action figures as large action figures. Based on this information, can the boy get 80 small action figures?
A. No, because he would not have enough tickets for 20 large action figures
B. Yes, because he would still have enough tickets for 320 large action figures
C. No, because he would not have enough tickets for 320 large action figures
D. Yes, because he would still have enough tickets for 20 large action figures
4L = s
7L + 3.5s = 380
Substitute 4L for s in the second equation and solve for L. Then solve for s.
From the values, make your choice of the alternatives.
To determine if the boy can get 80 small action figures with his 380 prize tickets, we need to calculate the number of large action figures he can exchange for tickets first.
According to the information given, 5 tickets can be exchanged for a large action figure. So, the number of large action figures he can get is the total number of tickets divided by 5:
Number of large action figures = 380 / 5 = 76
Now, let's calculate the number of small action figures he can get using the remaining tickets. We know that 7 tickets can be exchanged for 2 small action figures. Since he wants 4 times as many small action figures as large action figures, the number of small action figures can be determined as follows:
Number of small action figures = 4 * Number of large action figures
Number of small action figures = 4 * 76 = 304
Therefore, the total number of small action figures he can get using the remaining tickets is 304. Since he wanted to get 80 small action figures, it means he won't have enough tickets to exchange for all of them.
So, the correct answer is:
C. No, because he would not have enough tickets for 320 large action figures