Question

1. tickets to the zoo cost $12 for adults and $8 for children. the school has a budget of $240 for the field trip. an equation representing the budget for the trip is 240 = 12x + 8y. here is a graph of this equation. select all the true statements. a if no adult chaperones were needed, 30 students could go to the zoo. b. if ten students go to the zoo, then 15 adults can go. c. if four more adults go to the zoo, that means there will be room for six fewer students. d. if two more students go to the zoo, that means there will be room for three fewer adults. e. if 16 adults go to the zoo, then 6 students can go.

Explanation:

Step1: Analyze option A

Substitute \(x = 0\) (no adults) into \(240=12x + 8y\).

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Step2: Analyze option B

Substitute \(y = 10\) (10 students) into \(240=12x + 8y\).

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Step3: Analyze option C

The equation is \(240 = 12x+8y\), rewrite it as \(y = 30-\frac{3}{2}x\).
If \(x\) increases by \(4\) (new \(x=x_1 + 4\)), then new \(y_1=30-\frac{3}{2}(x + 4)=30-\frac{3}{2}x-6=y - 6\)

Step4: Analyze option D

Rewrite \(240=12x + 8y\) as \(x = 20-\frac{2}{3}y\).
If \(y\) increases by \(2\) (new \(y=y_1+2\)), then new \(x_1=20-\frac{2}{3}(y + 2)=20-\frac{2}{3}y-\frac{4}{3}
eq x-3\)

Step5: Analyze option E

Substitute \(x = 16\) into \(240=12x + 8y\).

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Answer:

A. If no adult chaperones were needed, 30 students could go to the zoo.
C. If four more adults go to the zoo, that means there will be room for six fewer students.
E. If 16 adults go to the zoo, then 6 students can go.