A restaurant sells basic lunches for $6 and supreme lunches for $8. You buy 12 lunches, represented by the equation x + y = 12,
where x is the number of basic lunches and y is the number of supreme lunches. The equation 6x + 8y = 88 represents the total cost. How many of each type of lunch did you buy?
1 answer:
1. Write out the equations that you have
6x + 8y = 88
x + y = 12
2. Isolate one variable is one equation. This is easiest in the second equation.
x + y = 12
-x -x
y = 12 - x
3. Plug this in for y in the other equation. Then solve that.
6x + 8 (12 - x) = 88
6x + 96 - 8x = 88
6x - 8x = -8
-2x = -8
x = 4
4. Find the other variable.
Since x = 4, that means we bought 4 basic lunches. Since we bought 12 in all, that must mean we bought 8 supreme lunches.
5. Double check by plugging in the numbers into the original equations.
6(4) + 8(8) = 88
24 + 64 = 88
88 = 88 (true)
4 + 8 = 12
12 = 12 (true)
6. Final answer
We bought 4 basic lunches and 8 supreme lunches.
6x + 8y = 88
x + y = 12
2. Isolate one variable is one equation. This is easiest in the second equation.
x + y = 12
-x -x
y = 12 - x
3. Plug this in for y in the other equation. Then solve that.
6x + 8 (12 - x) = 88
6x + 96 - 8x = 88
6x - 8x = -8
-2x = -8
x = 4
4. Find the other variable.
Since x = 4, that means we bought 4 basic lunches. Since we bought 12 in all, that must mean we bought 8 supreme lunches.
5. Double check by plugging in the numbers into the original equations.
6(4) + 8(8) = 88
24 + 64 = 88
88 = 88 (true)
4 + 8 = 12
12 = 12 (true)
6. Final answer
We bought 4 basic lunches and 8 supreme lunches.
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