Question

Andre and Mai need to enlarge two images for a group project. The two images are the same size. Mai makes a scaled copy of her image, increasing the lengths by 10%. It was still a little too small, so she increases the lengths by 10% again.

Andre says, “If I scale my image and increase the lengths by 20%, our images will be exactly the same size.”
In your own words, explain why Andre is incorrect.

Answer 1

10% twice will increase by 21%, not 20%

Explanation:

Increasing the length by 10% multiplies it by (1 +10%) = 1.10. Doing that again multiplies the length by that factor again, for a total multiplier of ...

(1.10)² = 1.21 = 1 +21%

Andre's image is increased by 20%, so its length is multiplied by (1 +20%) = 1.20. That is not exactly the same as 1.21 = 1 +21%.

Mai's image will be increased in length by 21%, which is not the same as 20%.