Question

Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts that have 360 calories each and $2 energy drinks that have 110 calories. This results in the following system of equations:

0.75d+2e≤25
360d+110e≥1,000

where d is donuts and e is energy drinks. Can Tension buy 8 donuts and 4 energy drinks?

Select the correct answer below:
Yes or No

Answer 1

Yes, he can buy 8 donuts and 4 energy drinks.

Explanation:

If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:

`0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25`

The first one is valid, since 14 is less than 25. Let's check the second one.

`360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000`

The second one is also valid.

Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.