If 1 burger equals 3 hot dogs and 2 burgers plus 4 hot dogs equals $20, what is the price of one hot dog? What is the price of one burger?

Question

I'm doing solving systems by substitution for math 1 grade 9.

Answer 1

Let B represent ONE BURGER.

Let H represent ONE HOT DOG.

If 1 burger equals 3 hot dogs: B = 3H

2 burgers plus 4 hot dogs equals $20: 2B + 4H = 20

Now we have two linear equations to solve at the same time. That's why we say, "SOLVING TWO LINEAR EQUATIONS SIMULTANEOUSLY".

You can solve using one of several methods: GRAPH, SUBSTITUTION, or ELIMINATION.

Let's use the SUBSTITUTION METHOD.

Since B = 3H in the top equation, each time we see a B in the bottom equation, we'll replace with 3H.

2B + 4H = 20 becomes 2(3H) + 4H = 20.

6H + 4H = 20 (Multiplying 2 times 3H.)

10H = 20

H = 2 (Dividing both sides by 10.)

Therefore, THE PRICE OF ONE HOT DOG IS $2.00

To determine the price of one burger, substitute the value of 2 into either the top or bottom equation

from above.

Let's use the top equation: B = 3H then becomes B = (3)(2) = $6

Therefore, THE PRICE OF ONE HAMBURGER is $6.00

CHECKING:

Does B = 3H? 6 = (3)(2) Yes, 6 = 6.

Does 2B + 4H = 20? (2)(6) + (4)(2) = 12 + 8 = 20 Yes, 2B + 4H = 20.