proportional tables
Proportional reasoning
constant of proportionality
100
Is the table proportional, explain.
No, because it does not have a constant rate of $4.35.
100
Jayden and Mia are comparing music streaming plans before summer break. Jayden's plan costs $71.46 for 9 months, while Mia's plan costs $96.25 for 11 months. Which plan has the lower cost per month, and how much cheaper is it each month?
Jayden's plan costs 71.46÷9=7.94 dollars per month. Mia's plan costs 96.25÷11=8.75 dollars per month. Jayden's plan has the lower cost, and it is 8.75−7.94=0.81 dollars cheaper per month.
100
Maya is helping her family compare cereal prices at the grocery store. One box of cereal costs $4.68 for 18 ounces. A larger box costs $6.72 for 24 ounces. What is the constant of proportionality for each box in dollars per ounce, and which cereal is the better buy?
For the first cereal box, the constant of proportionality is 4.68÷18=0.26 dollars per ounce. For the larger cereal box, the constant of proportionality is 6.72÷24=0.28 dollars per ounce. The first cereal box is the better buy because 0.26<0.28, so it costs less per ounce.
200
Is the table proportional? Explain.
Yes, it has the same unit rate of $2.65.
200
Elena is mixing sports drink for her soccer team during a weekend tournament. The recipe uses 3 scoops of powder for every 2 gallons of water. If Elena is filling a large cooler with 15 gallons of water, how many scoops of powder will she need to keep the flavor the same?
The ratio is 33 scoops for every 22 gallons. For 15 gallons, Elena needs 15× 1.5=22.5 scoops.
200
Elena is choosing between two packs of yogurt cups for after-school snacks. A 10-pack costs $8.90, and a 15-pack costs $12.60. Find the constant of proportionality for each option in dollars per cup. Then decide whether the prices are proportional in the same way or if one pack is the better deal.
For the 10-pack, the constant of proportionality is 8.90÷10=0.89 dollars per cup. For the 15-pack, the constant of proportionality is 12.60÷15=0.84 dollars per cup. The 15-pack is the better buy because 0.84<0.89, so each yogurt cup costs less.
300
Is the table proportional? Explain.
No, they do not have the same unit rate.
300
Marcus is saving up to buy a new gaming headset. He earns $84.50 for working 6.5 hours at his uncle's pet shop. If Marcus works 14.75 hours next week at the same rate, how much money will he earn?
Marcus earns 84.50÷6.5=13 dollars per hour. In 14.75 hours, he earns 14.75×13=191.75 dollars.
300
Jordan is comparing the price of grapes at two grocery stores before a family party. At Store A, 2.5 pounds of grapes cost $7.25. At Store B, 3.2 pounds of grapes cost $8.64. Find the constant of proportionality for each store in dollars per pound, and decide which store has the lower unit price.
For Store A, the constant of proportionality is 7.25÷2.5=2.90 dollars per pound. For Store B, the constant of proportionality is 8.64÷3.2=2.70 dollars per pound. Store B is the better buy because 2.70<2.90, so the grapes cost less per pound there.