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At Howdy Night, a student spends $45 and buys 25 items to share with her friends. Silly string is on sale for $3 and candy bars are sold for $1.50. How many bottles of silly string and how many candy bars did she buy?

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c + s = 25
1.50c +3s = 45

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s = number of silly string bottles
c = number of candy bars

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The final solution point is (20, 5), meaning the student, out of 25 items, bought 5 bottles of silly string and 20 candy bars with her $45.

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We plugged the original two equations into Desmos. The intersection is at (20, 5).

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STEPS:
1. Start with two equations.
c + s = 25
1.50c +3s = 45

2. Multiply the first equation by -3 to cancel out the s variables.
-3c + -3s = -75
1.50 c + 3s = 45

3. Cancel out the 3s and solve for c. Add -3c and 1.50c and -75 and 45.
-1.50c = -30

4. Divide by -1.50 on both sides to find c.
c = 20

4. Now, to solve for s, plug c back into the original equation c + s = 25.
20 + s = 25.

5. Subtract 20 to both sides to find s.
s = 5

So, the student bought a total of 5 silly string bottles and 20 candy bars with her $45 dollars.

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STEPS:
1. Start with two equations.
c + s = 25
1.50c +3s = 45

2. Isolate one variable. To isolate s, subtract c from both sides.
c + s= 25

-c        -c
s= -c + 25

3. Plug in the new equation for s into the second original equation from step 1.
1.50c + 3(-c+25) = 45

4. Distribute the 3.
1.50c -3c + 75 = 45

5. Combine like terms 1.50 c and -3c. Then, subtract 75 from both sides.
1.50c = 30

6. Divide both sides by 1.50.
c = 20.

7. Plug the answer for c into the first original equation from step 1.
20 + s = 25

8. Subtract 20 from both sides.
s = 5

Like in elimination,  the student bought a total of 5 silly string bottles and 20 candy bars with her $45 dollars.