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?
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.
d+h = 84
3d+4h = 285
Now crank 'er out.
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.
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
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns: let's say D represents the number of drinks sold and H represents the number of hot dogs sold.
From the information given, we know that the price of a drink is $3, so the revenue from drinks can be calculated as 3D. Similarly, the price of a hot dog is $4, so the revenue from hot dogs can be calculated as 4H.
We also know that the total number of items sold is 84, so we can write the first equation as:
D + H = 84 (equation 1)
Additionally, we know that the total revenue made is $285, so we can write the second equation as:
3D + 4H = 285 (equation 2)
Now we have a system of equations:
D + H = 84
3D + 4H = 285
There are various methods to solve this system. One simple and common approach is substitution. Let's solve equation 1 for D:
D = 84 - H
Now substitute this expression for D in equation 2:
3(84 - H) + 4H = 285
Simplify the equation:
252 - 3H + 4H = 285
H = 33
Substitute the value of H back into equation 1 to find D:
D + 33 = 84
D = 51
Therefore, Joe and Mo sold 51 drinks and 33 hot dogs.