Mass of the energy bar

Question

A food company that is developing a new energy bar has not decided on the size of the bar. The recipe includes 9% protein and 13% fat. The company wants the bar to contain at least 6g of protein and no more than 10g of fat. Use two inequalities to determine the possible range of masses for the bar.

Answer 1

Let x = the mass of the energy bar.

 

If the bar is composed of 9% protein, and it has to contain at least 6 gm of protein, then this can be expressed as:

 

0.09x ≥ 6

 

Why? Because 9% = 0.09, and "at least" corresponds to "greater than or equal to."

 

If the bar is to be composed of 13% fat, and it can contain no more than 10 gm of fat, then this inequality would be:

 

.13x ≤ 10

 

Why? We can convert 13% to 0.13, and "no more than" implies "less than or equal to."