Answer to Question #220820 in Algebra for Mash

Question

(3) Soso bought two cats, Gretchen and TK, from a pet store in 2015. Gretchen’s

weight was 3 kilograms, and TK 5 kilograms. In 2018, after a period of

growth, Gretchen weighed 6 kilograms and TK 8 kilograms.

2. Is Tawanda making an additive or multiplicative comparison?

Explain your reasoning.

(iii) Write a ratio that compares Gretchen’s kilograms in 2018 to Gretch￾en’s kilograms in 2015.

(iv) Write a ratio that compares TK’s kilograms in 2018 to TK’s kilograms

in 2015.

(v) Determine which cat gained more weight (grew bigger) using a

multiplicative comparison. Explain your reasoning.

Answer 1

In 2015,

Gretchen’s weight = 3 kilograms

TK = 5 kilograms

In 2018,

Gretchen weight = 6 kilograms

TK weight = 8 kilograms

2.

This is an additive and not a multiplicative comparison because 3 kilograms are added to both Gretchen and TK's weight

(iii)

The ratio that compares Gretchen’s kilograms in 2018 to Gretchen’s kilograms in 2015 $= \dfrac63 = \dfrac21 = 2 :1$

(iv)

The ratio that compares TK’s kilograms in 2018 to TK’s kilograms in 2015 $= \dfrac85 =8:5$

(v)

Gretchen's percentage weight change = $\begin{aligned}\\ \\&\dfrac{\textsf{Change in weight}}{\textsf{original/initial weight}} ×100\% \\ \\&=\dfrac{6-3}3 ×100\%= \dfrac33×100\% = 100\% \end{aligned}$

TK's percentage weight change =

$\begin{aligned}\\ \\&\dfrac{\textsf{Change in weight}}{\textsf{original/initial weight}} ×100\% \\ \\&=\dfrac{8-5}5 ×100\%= \dfrac35×100\% = 60\% \end{aligned}$

$\therefore$ While Gretchen's weight doubled, TK's weight only increased by 60%.

This means that Gretchen gained more weight (grew bigger) using a multiplicative comparison.