Question

sort the scenarios into the appropriate bins by whether or not they are proportional relationships. keyboard help questions |< proportional not proportional priya buys 2 pounds of turkey for $10.60 flora finds turkey for $4.99 a pound and uses a $1 off coupon perig pays $5.75 for one pound of turkey and $4.95 for the second. lily sees that turkey is on sale for $12.33 for 3 pounds.

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship has a constant ratio (unit rate) and passes through the origin (when one quantity is 0, the other is 0). The formula is \( y = kx \), where \( k \) is the constant of proportionality (unit rate).

Step2: Analyze Priya's Scenario

Priya buys 2 pounds for $10.60. The unit rate \( k=\frac{10.60}{2}=5.30 \) dollars per pound. If we check for \( x = 0 \) pounds, cost \( y = 0 \), and the ratio is constant. So this is proportional.

Step3: Analyze Flora's Scenario

Flora has $4.99 per pound plus a $1 off coupon. The cost function is \( y = 4.99x - 1 \). When \( x = 0 \), \( y=- 1
eq0 \), so it does not pass through the origin. Thus, not proportional.

Step4: Analyze Perig's Scenario

Perig pays $5.75 for the first pound and $4.95 for the second. The unit rate is not constant (5.75 vs 4.95), so the ratio changes. Not proportional.

Step5: Analyze Lily's Scenario

Lily has $12.33 for 3 pounds. Unit rate \( k=\frac{12.33}{3} = 4.11 \) dollars per pound. For \( x = 0 \), \( y = 0 \), and the ratio is constant. So this is proportional.

Answer:

Proportional:

• Priya buys 2 pounds of turkey for $10.60
• Lily says that turkey is on sale for $12.33 for 3 pounds

Not Proportional:

• Flora finds turkey for $4.99 a pound and uses a $1 off coupon
• Perig pays $5.75 for one pound of turkey and $4.95 for the second