a boy has 380 prize tickets he wants to exchange for action figures at a prize booth,the prize both tickets 5 tickets can be exchanged for a large figure and 7 tickets for 2 small figures the boy wants 4 times as many small action figures as large can the boy get 80 small action figures
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So we know he has 380 tickets overall and needs 5 for one large action figure and 7 for 2 small action figures. As for the amount he wants, he wants 4 times as many small ones than large ones. Due to how we know the solution of if he can get 80 small action figures, simply put, that would be 80 / 4 = 20. So that means 80 small and 20 large. Now we need to figure out how many tickets that is.
80 / 2 = 40 x 7 = 280 tickets. 20 x 5 = 100 tickets. That equals exactly 380 tickets. So the answer is yes, he can get 80 small action figures.
To determine if the boy can get 80 small action figures, we need to calculate if he has enough tickets to exchange for them.
Let's assume the boy exchanges x large figures and y small figures.
The number of tickets required for x large figures is 5x.
The number of tickets required for y small figures is 7y.
According to the problem, the boy wants 4 times as many small action figures as large, so we can represent this as: y = 4x.
We have the total number of tickets available: 380.
Therefore, we can write the equation: 5x + 7y = 380.
Substituting y = 4x into the equation, we get: 5x + 7(4x) = 380.
Simplifying the equation, we have: 5x + 28x = 380.
Combining like terms, we get: 33x = 380.
Dividing both sides by 33, we get: x = 11.515.
Since we cannot have a fraction of an action figure, we need to round the value of x down to the nearest whole number: x = 11.
Substituting x = 11 into the equation y = 4x, we get: y = 4(11) = 44.
Therefore, the boy can get 11 large figures and 44 small figures.
To determine the total number of small figures, multiply the number of large figures by 4: 11 * 4 = 44.
Since the boy wants 80 small action figures, and he can only get 44, he cannot get 80 small action figures.
To determine whether the boy can get 80 small action figures with his 380 prize tickets, we need to break down the exchange rates and calculate the number of figures he can get.
Given:
- 5 tickets can be exchanged for a large figure.
- 7 tickets can be exchanged for 2 small figures.
- The boy wants 4 times as many small action figures as the large ones.
Let's calculate the number of large figures the boy can get. Since 5 tickets can be exchanged for a large figure, we divide the total number of tickets (380) by 5:
Large figures = 380 tickets / 5 tickets = 76 large figures
Now, let's calculate the number of small figures the boy can get. Since 7 tickets can be exchanged for 2 small figures, we need to calculate the number of small figures the boy can get per ticket:
Small figures per ticket = 2 figures / 7 tickets = 2/7 figures per ticket
As the boy wants 4 times as many small figures as large ones, we multiply the number of large figures (76) by 4:
Desired number of small figures = 76 large figures * 4 = 304 small figures
Now, let's calculate the number of tickets needed to get that many small figures:
Required number of tickets for small figures = Desired number of small figures / Small figures per ticket
= 304 small figures / (2/7 figures per ticket)
= 304 small figures * (7/2) ticket per figure
= 1064 tickets
As we can see, the boy would need 1064 tickets to get 304 small action figures, which is more than the 380 tickets he has. Therefore, the boy cannot get 80 small action figures with his 380 prize tickets.