Question

joe and mo sold drinks and hot dogs. drinks were $3 and hit dogs were $4. They sold a total of 84 items and made a total of $285. How many drinks and how many hot dogs did they sell?

Answer 1

Let d = the number of drinks sold

Let h = the number of hot dogs sold

the total number of items sold = the number of drinks sold + the number of hot dogs sold = d + h = 84

The total amount of money made equals the money made selling drinks plus the money made selling hot dogs = $285

The money made selling drinks = the cost of a drink times the number of drinks sold = $3d

The money made selling hot dogs = the cost of a hot dog times the number of hot dogs sold = $4h

The total amount of money made = $3d + $4h = $285

This gives us 2 equations and two unknowns

d + h = 84

and

3d + 4h = 285

Solving by substitution:
Solve the first equation for d or h
d + h = 84
d = 84 - h

Substitute into the second equation
3d + 4h = 285
3(84 - h) + 4h = 285

Solve for one variable.
3(84) - 3h + 4h = 285
252 + h = 285
h = 285 -252 = 33

Substitute the solution back into the first equation to solve for the 2nd variable
d + h = 84
d + 33 = 84
d = 84-33 = 51

Check your answer by substituting the solution into the 2nd equation
3d + 4h = 285
3(51) + 4(33) = 153 + 132 = 285

Answer the question
They sold 51 drinks and 33 hot dogs.

Answer 2

d+h = 84
3d+4h = 285
Now crank 'er out.

Answer 3

Use x to represent the number of drinks sold and use y to represent the number of hot dogs sold.

Then x+y=84 and 3x+4y=285.
Now subtract y from both sides of the first equation to get x=84-y.
Then substitute this into the second equation to get 3(84-y)+4y=285.
Distribute and combine like terms to get 252-3y+4y=y+252=285.
Subtract 252 from both sides to get y=33.
Substitute back into the first equation to get x+33=84.
Subtract 33 from both sides to get x=51.
So Joe and Mo sold 51 drinks and 33 hot dogs.

You can check your work by multiplying 51⋅$3=$153, and 33⋅$4=$132, then adding $153+$132=$285.

Answer 4

3D + 4H = 285

D+H = 84

3D + 3H = 252

subtract that last equation from the 1st to eliminate D and solve for H

H = 33 hot dogs sold

D = 84 -33 = 51 drinks sold

33(4) + 51(3) = 132 + 153 = 285