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Chapter 11: Problem 5

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase? a. 35 b. 45 c. 72 d. 199 e. 208

Short Answer

Expert verified
The correct answer is not listed among the options given. The customer purchases 245 small cans.

Step by step solution

01

Define the variables

Let's define the cost of a small can as \(s\), a medium can as \(m\) and a large can as \(l\). The given problem implies that \(l = 5m = 7s\). Therefore we can say that the price of a medium can is \(m = l / 5 = 7s / 5 \) and the price of a small can is \(s = l / 7\).
02

Set up the equation

According to the second statement the cost for an equal number of small and large cans is equal to the cost of 200 medium cans, we can write this as \(nl + ns = 200m\) where \(n\) is the number of large and small cans.
03

Simplify the equation

We can substitute the values of s, m in terms of l obtained from step 1 into the equation from step 2. We get \(nl + nl/7 = 200*7l/5 \rightarrow l*(8/7)n = 280l\).
04

Solve for n

Since l is a common factor, we can cancel it out and solve the equation to get the number of cans. This gives \(n = 280 * 7/8 = 245 cans\)

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