Answer:
35 hotdogs and 52 sodas were sold.
Step-by-step explanation:
Create equations to represent the problem.
let "d" be the number of hotdogs sold
let "a" be the number of sodas sold
1.5d + 0.5a = 78.50 Equation for money made
d + a = 87 Equation for items sold
Rearrange d + a = 87 to isolate one of the variables.
a = 87 - d
Substitute a for 87-d into the other equation. Isolate using reverse operations.
1.5d + 0.5a = 78.50
1.5d + 0.5(87 - d) = 78.50 Distribute over brackets by multiplying
1.5d + 43.5 - 0.5d = 78.50 Collect like terms
43.5 + d = 78.50 1.5d - 0.5d is 1d. You don't need to write "1".
43.5 + d - 43.5 = 78.50 - 43.5 Isolate d, subtract 43.5 from both sides
d = 35 Number of hotdogs sold
Substitute d for 35 in the simpler equation
d + a = 87
35 + a = 87 Subtract 35 form both sides to isolate "a".
a = 87 - 35
a = 52 Number of sodas sold
Therefore 35 hotdogs and 52 sodas were sold.
