Raj and his friends went to the movies today and ate 875 pieces of popcorn, or 125% more than they ate when they went to the movies last week.

Question

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 125 Over 100 EndFraction = StartFraction 875 Over question mark EndFraction.

Which steps can be used to find how much popcorn Raj and his friends ate at the movies last week?

Check all that apply.
125 + 750 = 875
125 × 7 = 875
100 × 7 = 700 pieces of popcorn
100 + 750 = 850 pieces of popcorn
125 + 875 = 1000 pieces of popcorn

Answer 1

To find out how much popcorn Raj and his friends ate at the movies last week, we can first understand that they ate 875 pieces of popcorn this week, which is 125% more than what they ate last week.

This means that if we let $x$ represent the amount of popcorn they ate last week, then according to the problem:

1. 100% of last week's popcorn is $x$.
2. 125% more than $x$ means they ate $x+1.25x=2.25x$.
3. We know that $2.25x=875$.

To solve for $x$:

$$x=\frac{875}{2.25}$$ Calculating $2.25$ as a fraction gives us $\frac{9}{4}$: $$x=875\times \frac{4}{9}$$ Calculating that gives: $$x=\frac{3500}{9}=388.89$$ However, we can also use simpler steps to arrive at the total popcorn eaten last week.

Now, let's review the options you provided:

1. 125 + 750 = 875 - This is incorrect.
2. 125 × 7 = 875 - This is incorrect.
3. 100 × 7 = 700 pieces of popcorn - This is correct. Last week they ate 700 pieces (which is 100% of the popcorn).
4. 100 + 750 = 850 pieces of popcorn - This is incorrect, as it does not relate to the amounts involved.
5. 125 + 875 = 1000 pieces of popcorn - This is also incorrect, as it does not relate to the question.

Based on the steps reviewed, the only option that correctly helps to find how much popcorn they ate last week is:

3. 100 × 7 = 700 pieces of popcorn.