Question

Michelle spent $32 on hot dogs and hamburgers. Hot dogs were $5 and hamburgers $6. If she bought a total of 6 items, how many of each kind did she buy?

Michelle spent $32 on hot dogs and hamburgers. Hot dogs were $5 and hamburgers $6. [ If she bought a total of 6 items, Michelle buys 4 hot dogs and 2 hamburgers. Solution: x + y = 6; 5x + 6y = 32; 6x + 6y - (5x + 6y) = 36 - 32; x = 4, Put x= 4 in (1), we have, y = 6 - 4; y= 2. ]

Answer 1

Michelle bought 2 hamburgers and 4 hot dogs

Explanation:

As you've already implied, we will need a system of equations to find the amount of hot dogs and hamburgers Michelle bought.

First equation: We can allow x to represent the number of hot dogs and y the number of hamburgers. Since she bought 6 items altogether, our first equation is x + y = 6, since:

quantity of hot dogs + quantity of hamburgers = total amount of food

Second equation: Since she spent $32 altogether, hot dogs cost $5, and hamburgers cost $6, our second equation is 5x + 6y = 32 since:

(price of hot dogs * quantity) + (price of hamburgers* quantity) = total cost.

Method to solve the system: Substitution: Isolate x in the first equation and plug it in for x in the second equation to solve for y:

If we isolate x in the first equation, we get x = -y + 6.

Now we can plug in x = -y + 6 for x in the second equation to first solve for y, the number of hamburgers she bought:

5(-y + 6) + 6y = 32

-5y + 30 + 6y = 32

y + 30 = 32

y = 2

Plug in 2 for y in any of the two equations to solve for x:

We can now plug in 2 for y in the first equation to find x, the number of hot dogs she bought:

x + 2 = 6

x = 4

Thus, Michelle bought 2 hamburgers and 4 hot dogs.