Question

solve & discuss it!
scott is making a snack mix using almonds and raisins. for every 2 cups of almonds in the snack mix, there are 3 cups of raisins. ariel is making a snack mix that has 3 cups of almonds for every 5 cups of sunflower seeds. if scott and ariel each use 6 cups of almonds to make a batch of snack mix, who will make a larger batch?
scott’s almonds
scott’s raisins
ariel’s almonds
ariel’s sunflower
represent and connect how can you use ratio tables to represent scott’s and ariel’s snack mixes?

Explanation:

Step1: Calculate Scott's raisins

Scott's ratio of almonds to raisins is \(2:3\). Let the number of raisins be \(x\) when almonds are 6 cups. So, \(\frac{2}{3}=\frac{6}{x}\), cross - multiply: \(2x = 6\times3\), \(2x=18\), \(x = 9\). Total for Scott: \(6 + 9=15\) cups.

Step2: Calculate Ariel's sunflower seeds

Ariel's ratio of almonds to sunflower seeds is \(3:5\). Let the number of sunflower seeds be \(y\) when almonds are 6 cups. So, \(\frac{3}{5}=\frac{6}{y}\), cross - multiply: \(3y=6\times5\), \(3y = 30\), \(y = 10\). Total for Ariel: \(6+10 = 16\) cups.

Step3: Compare the totals

Scott's total is 15 cups, Ariel's total is 16 cups. Since \(16>15\), Ariel's batch is larger.

Answer:

Ariel will make a larger batch.