Question

7.5.13 problem 4
two students are both working on the same problem: a box of laundry soap has 25% more soap in its new box. the new box holds 2 kg. how much soap did the old box hold?

• here is how jada set up her double number line.

soap (kg) <------------------1.5----2----------------->

<------------------75%----100%----------------->

• here is how lin set up her double number line.

soap (kg) <------------------1.6----2----------------->

<------------------100%----125%----------------->
17 multiple choice 1 point
do you agree with either of them? explain or show your reasoning in your workbook.
○ i agree with jada.
○ i agree with lin.

Explanation:

Step1: Understand the Problem

The new box has 25% more soap than the old box, and the new box holds 2 kg. We need to find the old box's soap amount and check the double number lines.

Step2: Analyze Lin's Double Number Line

Lin's number line has 100% (old box) and 125% (new box, since 100% + 25% = 125%). Let the old box be \( x \) kg. Then \( 1.25x = 2 \). Solving for \( x \): \( x=\frac{2}{1.25}=1.6 \) kg. Lin's soap line has 1.6 (100%) and 2 (125%), which matches.

Step3: Analyze Jade's Double Number Line

Jade's percentage line has 75% and 100%, and soap line 1.5 and 2. If 100% is 2, then 75% should be \( 0.75\times2 = 1.5 \), but this is about the old box? No, the new is 25% more than old, so old is 100%, new 125%. Jade's percentage scale is wrong (75% vs 100% doesn't relate to 25% increase).

Answer:

I agree with Lin.