Question

Monica and Lauren plan to buy some of their dry ingredients (particularly flour, sugar, and

baking soda) in prepackaged containers. Each container with the three dry ingredients weighs

22 pounds. The weight of the sugar in each container is 2 times the amount of baking soda.

Also, there are 14 pounds more flour than baking soda in each container.

The girls want to calculate the weight of baking soda in each container, but they claim that the

necessary equation is impossible because it has infinitely many solutions.

Identify an equation that proves the girls' claim is wrong and explain why that equation does not

have infinitely many solutions.

Answer 1

Weight of baking soda in each container = 2 pounds

Weight of sugar in each container = 4 pounds

Weight of flour in each container = 16 pounds

Explanation:

As given,

Let the weight of baking soda in each container = x pounds

Given that,

The weight of the sugar in each container is 2 times the amount of baking soda.

⇒ Weight of sugar in each container = 2x

Also given,

There are 14 pounds more flour than baking soda in each container

⇒Weight of flour in each container = 14 + x

Now,

Given that each container with the three dry ingredients weighs 22 pounds.

⇒ x + 2x + 14 + x = 22

⇒4x + 14 = 22

⇒4x = 22 - 14

⇒4x = 8

⇒x =
`(8)/(4)` = 2

∴ we get

Weight of baking soda in each container , x = 2 pounds

⇒Weight of sugar in each container , 2x = 2(2) = 4 pounds

and Weight of flour in each container , 14+x = 14 + 2 = 16 pounds

As we have found the value of x is unique , so it can not be possible to have infinite solutions. So, the girl's claim is wrong.