At the local market, Bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while Sarah buys 2 juice boxes and 1 hot dog at a cost of $5.

Question

i really need help to answer this

Answer 1

This is a modest linear system question. We know because the same items are gathered in two different ways. Let's assume the cost of each item was your question (you didn't include it). In that case, we will use:

J - cost of juice box

H = cost of hot dog

That means we have the system:

3J + 2H = 8

2J + 1H = 5

You could use either substitution or addition (sometimes called "elimination" in your books). In this case, substitution would be easier, so let's run with that. First, we must solve for one letter in one equation. I say the "H" in equation two:

2J + 1H = 5

-2J          -2J

        H = 5 - 2J

Now we substitute into the first equation:

3J + 2(5 - 2J) = 8

3J + 10 - 4J = 8

 -J  + 10 = 8

        -10    -10

    -J      = -2

    /-1      /-1

     J = 2

Now we can substitute back into our previous equation for H:

H = 5 - 2J

H = 5 - 2(2)

H = 5 - 4 = 1

Ordered pairs are always written in alphabetical order, so the answer is: (1, 2)