Question

1. at the high school football game, a student purchased 3 tacos and 7 pieces of sour hard candy for $6.60. a second student purchased 4 tacos and 8 pieces of sour hard candy for $8.40. how much does it cost for each item?

Explanation:

Step1: Define variables for items

Let $t$ = cost of 1 taco, $c$ = cost of 1 candy piece.

Step2: Set up system of equations

$$3t + 7c = 6.60$$
$$4t + 8c = 8.40$$

Step3: Simplify the second equation

Divide the second equation by 4:
$$t + 2c = 2.10$$
Rearrange to isolate $t$:
$$t = 2.10 - 2c$$

Step4: Substitute $t$ into first equation

$$3(2.10 - 2c) + 7c = 6.60$$
Expand and simplify:
$$6.30 - 6c + 7c = 6.60$$
$$6.30 + c = 6.60$$

Step5: Solve for $c$

$$c = 6.60 - 6.30 = 0.30$$

Step6: Solve for $t$ using $c$

$$t = 2.10 - 2(0.30) = 2.10 - 0.60 = 1.50$$

Answer:

1 taco costs $\$1.50$, and 1 piece of sour hard candy costs $\$0.30$