Question

A grocery store sells boxes of two kinds of cereals, wheat-based and rice-based. In this store, the average weight of a box of rice-based cereal is 60 ounces, the average weight of a box of wheat-based cereal is 48 ounces, and the average weight of all the boxes of cereal is 50 ounces. What is the ratio in this store of boxes of rice-based cereals to wheat-based cereals?

Answer 1

Answer:

The ratio of rice-based cereals to wheat-based cereals is 1/5

Step-by-step explanation:

In this problem, we know the weight of both kind of boxes of cereal and also the average weight of the total amount of boxes in the grocery store.

However, we don't know how many boxes of each kind are there in the store and we need to figure out what the ratio is.

Data:

Wheat-based cereal box weight = 48 ounces

Rice-based cereal box weight = 60 ounces

Average weight of total boxes = 50 ounces

Let's name

$x=$ number of wheat-based boxes of cereal.

$y=$number of rice-based boxes of cereal.

The total weight of the wheat and rice cereals would be $48x+60y$

We know that the average weight is a division between the total amount of weight and the amount of items we have, algebraically and based on the previous expression, we would write the equation this way:

$\frac{48x+60y}{x+y} =50$

Solving the equation we get:

$48x+60y=50(x+y)\\ 48x+60y =50x+50y\\ 60y-50y=50x-48x\\ 10y=2x\\ \frac{y}{x}=\frac{2}{10}\\ \frac{y}{x}=\frac{1}{5}$

Therefore, the ratio in this store of boxes of rice-based cereals to wheat-based cereals is 1/5