Question

Please solve this for me and show steps that would be a big help!

Answer 1

• bagel: $3
• OJ: $2

Explanation:

You want the price of a bagel and a can of OJ if 2 bagels and 1 can costs $8, and 3 bagels and 2 cans cost $13.

Equations

You can write an equation for the value of each purchase. The cost of a bagel can be represented by 'b', and 'j' can be used for the cost of an orange juice.

• 2b +1j = 8
• 3b +2j = 13

Solution

The coefficients of j are related by a factor of 2, so we can make the sum of coefficients of j be zero if we subtract the second equation from 2 times the first:

2(2b +1j) -(3b +2j) = 2(8) -(13)

b = 3 . . . . . . . . . . . . . . simplify

Now, we can use this value in the first equation to find j:

2(3) +1j = 8

1j = 2 . . . . . . . . . subtract 6

A bagel costs $3, and a can of orange juice costs $2.