Question

and table show the total cost of the number of sessions attended, x. pottery class: y = 10x + 15
number of sessions: 0, 1, 2, 3, 4
total cost for pottery ($): 15, 25, 35, 45, 55
drawing class:
number of sessions: 0, 1, 2, 3, 4
total cost ($): 0, 16, 32, 48, 64
how many sessions can you take for the pottery class to cost less?
choose all that apply.
1
2
3
4

Explanation:

Step1: Find Drawing Class Cost Function

The Drawing Class has a total cost of $0$ for $0$ sessions, $16$ for $1$, $32$ for $2$, etc. The rate is $16$ per session, so its cost function is $y = 16x$.

Step2: Set Up Inequality for Pottery < Drawing

Pottery cost: $y = 10x + 15$. We need $10x + 15 < 16x$.

Step3: Solve Inequality

Subtract $10x$: $15 < 6x$. Divide by $6$: $2.5 < x$. Since $x$ is number of sessions (integer), $x \geq 3$. But check options: 1,2,3,4. Wait, maybe miscalculation. Wait, let's check each session:

• Session 1: Pottery: $10(1)+15=25$, Drawing: $16(1)=16$. $25 > 16$ → no.
• Session 2: Pottery: $35$, Drawing: $32$. $35 > 32$ → no.
• Session 3: Pottery: $45$, Drawing: $48$. $45 < 48$ → yes.
• Session 4: Pottery: $55$, Drawing: $64$. $55 < 64$ → yes.

Wait, earlier inequality: $10x +15 < 16x$ → $15 < 6x$ → $x > 2.5$. So $x=3,4$ (since $x$ is integer sessions). But wait, when $x=3$: $45 < 48$ (true), $x=4$: $55 < 64$ (true). $x=1$: $25 < 16$? No. $x=2$: $35 < 32$? No. So correct options are 3 and 4? Wait, but let's recheck the tables:

Pottery table: x=0:15, x=1:25, x=2:35, x=3:45, x=4:55.

Drawing table: x=0:0, x=1:16, x=2:32, x=3:48, x=4:64.

So for x=1: Pottery 25 vs Drawing 16 → Pottery more.

x=2: 35 vs 32 → Pottery more.

x=3: 45 vs 48 → Pottery less.

x=4: 55 vs 64 → Pottery less.

So the sessions where Pottery costs less are 3 and 4. But the options are 1,2,3,4. So the correct ones are 3 and 4? Wait, but the problem says "Choose ALL that apply" with options 1,2,3,4. Wait, maybe I made a mistake in the inequality. Wait, maybe the question is "cost less than drawing class"? Wait, let's re-express:

We need Pottery Cost < Drawing Cost.

For x=1: 25 < 16? No.

x=2: 35 < 32? No.

x=3: 45 < 48? Yes.

x=4: 55 < 64? Yes.

So the correct options are 3 and 4. But the options given are 1,2,3,4 (buttons). So the answer is 3 and 4? Wait, but let's check again. Wait, maybe the inequality was reversed? Wait, no: Pottery cost is $10x +15$, Drawing is $16x$. So when is $10x +15 < 16x$? As before, $x > 2.5$. So x=3,4. So the applicable sessions are 3 and 4.

Answer:

3, 4 (the options with "3" and "4" as the number of sessions)