Question

1. matching: systems of inequalities (bubble gum & mints)

ms. wallace-el wants to buy bubble gum and mints for her students. use the information below to
determine the number of bubble gum packs and mints she can buy.

• bubble gum costs $0.40 per pack.
• mints cost $0.80 each.
• ms. wallace-el can spend no more than $64 total.
• she needs to buy at least 3 times as many packs of bubble gum as mints.

let:

• ( x ) = number of packs of bubble gum
• ( y ) = number of mints

directions:
match each statement in column a with the correct inequality or value in column b.
write the letter of the correct answer next to each number.

column a

1. the inequality that represents the total cost constraint.
2. the inequality that represents the quantity requirement.
3. the complete system of inequalities that models the situation.
4. if ms. wallace-el buys 60 packs of bubble gum, the maximum number of mints she can buy.

column b
a. ( 0.40x + 0.80y leq 64 )
b. ( x geq 3y )
c. (\begin{cases} 0.40x + 0.80y leq 64 \\ x geq 3y end{cases})
d. 20
e. ( y geq 3x )

matching boxes for 1,2,3,4 with dashed boxes

Explanation:

Step1: Match total cost constraint

Total cost: $0.40x + 0.80y \leq 64$

Step2: Match quantity requirement

Bubble gum ≥ 3×mints: $x \geq 3y$

Step3: Match full system of inequalities

Combine the two constraints:

$$\begin{cases} 0.40x + 0.80y \leq 64 \\ x \geq 3y \end{cases}$$

Step4: Calculate max mints for x=60

Substitute $x=60$ into cost inequality:
$0.40(60) + 0.80y \leq 64$
$24 + 0.80y \leq 64$
$0.80y \leq 40$
$y \leq 50$
Wait, correction: Recheck calculation:
$0.4*60=24$, $64-24=40$, $40/0.8=50$. But wait, also apply quantity rule $60\geq3y \implies y\leq20$. The stricter constraint is $y\leq20$.

Answer:

1. A. $0.40x + 0.80y \leq 64$
2. B. $x \geq 3y$
3. C.

$$\begin{cases} 0.40x + 0.80y \leq 64 \\ x \geq 3y \end{cases}$$

1. D. 20