Question

Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.

Mangos Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz


Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1:8, and the ratio of smoothie size to mangos used for Bri is 3:24.
The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 64:3, and the ratio of smoothie size to mangos used for Angela is 64:4.

Answer 1

Based on the data provided in the table, the correct statement is:

The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

To determine the ratio, we need to compare the smoothie size to the number of mangos used for each person.

For Kim, the ratio of smoothie size to mangos used is 8:1, as she used 1 mango for an 8 oz smoothie.

For Bri, the ratio is 24:3, as she used 3 mangos for a 24 oz smoothie.

For Angela, the ratio is 32:4, as she used 4 mangos for a 32 oz smoothie.

If we simplify the ratios, we find that:

Kim's ratio simplifies to 8:1.

Bri's ratio simplifies to 8:1.

Angela's ratio simplifies to 8:1.

Since both Bri and Angela have the same ratio of 8:1, the correct statement is that the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

Answer 2

B) The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

Explanation:

The given table shows the number of mangos that were used for each of the different sizes of smoothies that the Kim, Bri and Angela ordered:

`\begin{array}c\cline{1-3}\vphantom{\frac12} &\sf Mangos\;Used & \sf Smoothie\;Size\\\cline{1-3}\vphantom{\frac12} \sf Kim & 1&8\; \sf oz\\\cline{1-3}\vphantom{\frac12} \sf Bri &3&24\; \sf oz\\\cline{1-3}\vphantom{\frac12} \sf Angela &4&32\; \sf oz\\\cline{1-3}\end{array}`

The ratios of smoothie size to mangos for Kim and her friends are:

`\begin{aligned}\sf Person&=\sf smoothie\;size:mangos\\\sf Kim &= 8 : 1\\\sf Bri &= 24 : 3\\\sf Angela &= 32 : 4\end{aligned}`

The ratios of Bri and Angela can be reduced to their simplest form by dividing both sides of the ratio by the greatest common factor:

`\sf Bri = 24 : 3 = (24)/(3):(3)/(3)=8:1`

`\sf Angela = 32: 4= (32)/(4):(4)/(4)=8:1`

Therefore, the ratio of smoothie size to mangos for Kim, Bri and Angela is the same (8 : 1).

The statement that is correct based on the data is:

• B) The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.