A paint mixture uses 2 cups of blue paint for every 5 cups of yellow paint to make green. If a painter has 6 cups of blue paint, how many cups of yellow paint are needed?
Model Support: Draw 2 boxes for blue and 5 equal boxes for yellow. If the 2 blue boxes equal 6 cups, how much does each single box represent?
Sentence Starter: "Since each box represents ___ cups, the 5 yellow boxes equal ___ cups."
Show your tape diagram or number line here:
A cafeteria makes fruit punch using orange juice and pineapple juice in a ratio of 3 : 4. If the cafeteria prepares 35 total gallons of punch, determine the exact number of gallons of orange juice and pineapple juice required.
Show your full calculation and mathematical justification:
Student Alex was asked to find a ratio equivalent to 4 : 7 with a first term of 16. Alex answered '16 : 19' explaining: 'I added 12 to 4 to get 16, so I added 12 to 7 to get 19.'
Scholar Analysis Task: Identify the flawed thinking in Alex's logic. Explain why ratios require multiplicative reasoning rather than additive change.
Explain the misconception and write the correct generalized solution: