three teenagers can eat 6 pizzas in half an hour. Assuming that their friends eat at the same rate, how many pizzas can 5 teenagers eat in 90 minutes?
6pizza/(3teen*.5hr) = 4pizza/(teen-hr)
so, that's 4 pizzas per hour per teen
take that and use the given data to get the final number of pizzas:
4pizza/(teen*hr) * 5teen * 1.5hr = 30pizza
To find out how many pizzas 5 teenagers can eat in 90 minutes, we can set up a proportionality equation based on the information given.
First, let's determine the rate at which three teenagers can eat pizzas in half an hour. We know that three teenagers can eat 6 pizzas in half an hour, so we can write this as a ratio:
(3 teenagers)/(6 pizzas) = (t) teenagers / (0.5) hours
Now, let's determine the rate per teenager per hour. To do this, we need to divide the ratio by the number of teenagers:
(3 teenagers)/(6 pizzas) ÷ 3 = (t) teenagers / (0.5) hours ÷ 3
Simplifying, we get:
1 teenager / 2 pizzas = (t) teenagers / (0.5) hours ÷ 3
Now, we can find the rate at which 1 teenager can eat pizzas in 1 hour:
(1 teenager) / (2 pizzas) = (t) teenagers / (0.5) hours ÷ 3 × 1 hour
Simplifying, we get:
1 teenager / 2 pizzas = (t) teenagers / (1.5) hours
Now, we can use this ratio to find out how many pizzas 5 teenagers can eat in 90 minutes:
(5 teenagers) / (x pizzas) = (1 teenager) / (2 pizzas)
By cross-multiplying, we get:
(5 teenagers) × (2 pizzas) = (1 teenager) × (x pizzas)
10 pizzas = x pizzas
Therefore, 5 teenagers can eat 10 pizzas in 90 minutes.