At a smoothie stand, each non-Vegan smoothie has 190 calories more than the Vegan smoothies. During a certain hour, five (5) Vegan smoothies and nine (9) non-Vegan smoothies were sold.

Question

At a smoothie stand, each non-Vegan smoothie has 190 calories more than the Vegan smoothies. During a certain hour, five (5) Vegan smoothies and nine (9) non-Vegan smoothies were sold.

If five (5) Vegan smoothies and nine (9) non-Vegan smoothies have a total of 7,450 calories, how many calories are in each non-Vegan smoothie?

Answer 1

Let me start by saying that I agree 100 percent with the solution presented by Mark C. I would simply like to point out an alternative approach for those students who would get as far as solving for x and then choose the trick answer that corresponded to that value, which I guarantee would show up in the responses.

Another approach: Track non-vegan smoothies the whole time, since the question asks about non-vegan smoothies. This will ensure that you do NOT answer the question that is not being asked. Let n stand for "non-vegan" and set up a similar system of equations to the ones Mark showed:

n = vegan smoothie + 190, so a vegan smoothie = n - 190 (This will help with substitution later.)

5 vegan smoothies + 9n = 7,450

Replacing "vegan smoothies" with its mathematical equivalent from above gives us

5(n - 190) + 9n = 7,450

5n - 950 + 9n = 7,450 (Distribute the 5.)

14n - 950 = 7,450 (Combine like terms on the left-hand side.)

14n = 8,400 (Add 950 to both sides.)

n = 600 (Divide both sides by 14. To go a little faster, just divide 84 by 14 and add back the zeros after the 6.)

I have seen too many students initially fall for a trap answer, and such mistakes can be both repetitive and costly over nearly 60 math questions. Keeping information organized and making sure you are answering the question being asked can add loads of points to your score.

Good luck with your studies.

Andrew

Answer 2

Let x = # of calories in Vegan Smoothies

Let x+190 = # of calories in Non-Vegan Smoothies

We know that five (5) Vegan Smoothies AND nine (9) Non-Vegan Smoothies, have a total of 7,450 calories. Put this into an equation, given what we already know:

5x + 9(x + 190) = 7,450

5x + 9x + 1,710 = 7,450 [Collect like terms]

14x + 1,710 = 7,450 [Deduct 1,710 from both sides, to isolate the x-value]

14x = 5,740 [Divide both sides by 14, to solve for 'x']

x = 410 [So, the Vegan Smoothies each have 410 calories. [BUT, we are asked about the number of calories for the Non-Vegan Smoothies, which is 190 additional calories each]

non-Vegan Smoothie calories: x + 190 = 410 + 190 = 600 calories

So, each non-Vegan Smoothie has 600 calories

[600]