Eliza's puppy weight?

Question

Eliza's puppy weighed 22 kilograms at 12 months of age. This is a 120% gain from its weight at 6 months. Eliza used these steps to find the puppy's weight at 6 months, but made an error.

 

Step 1: let x represent the puppy's weight at 6 months

 

Step 2: x+ 120/100=22

 

Step 3: x+1.2=22

 

Step 4: x= 22-1.2

 

Part A1: In which step did Eliza make an error?

 

Part A2: Explain what Eliza did wrong in the step where an error occurred

 

Part B: What was the puppy's actual weight at 6 months?

Answer 1

Part A

Step 1 is correct

Step 2 is incorrect; the equation should be x + x · 120/100 = 22kg

As a result of the error in step 2, the equations in steps 3 and 4 yield incorrect answers

 

Part B

 x + x · 120/100 = 22kg

x + 1.2x = 22kg

2.2x = 22kg

x = 10kg

 

Proof: x + x · 120/100 = 22kg; 10 + 10 · 1.2 = 22kg; 10 +12 = 22kg