A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each.

Question

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Answer 1

First, make two equations. Let X represent the jam and Y represent the bread mix. Since we know there are 8 items total, let the first equation show the number of items. X+Y=8. Next, let the second equation show the cost of the items. The jam (X) costs $6 and the bread mix (Y) costs $5. The total cost is $45. So the second equation is 6X+5Y=45. Use the substitution method to solve.

X+Y=8

6X+5Y=45

First, isolate X in the first equation, to make it X=8-Y

Now, substitute that for X in the second equation. 6(8-Y)+5Y=45

1. Multiply each term in the parenthesis by 6. 48-6Y+5Y=45. Now combine like terms.
2. 48-Y=45. Subtract 48 from each side
3. -Y=-3. Multiply both sides by -1 to make it positive
4. Y=3

Now, substitute 3 for Y in the first equation.

X+3=8. Subtract 3 from both sides

X=5

Now check your work. Plug the numbers into both equations to see if it's true.

5+3=8

6(5)+5(3)=45

Answer 2

Hi Cecelia,

You need to think of two numbers that when added together equal 45.

One of those two numbers needs to be a multiple of 6 in order to figure out how many jars of jam are in the basket.

The other number needs to be a multiple of 5 in order to figure out how many packages of bread mix are in the basket.

The multiple of 6 + the multiple of 5 = 45.

Once you figure out each of the two given multiples, you will then be able to figure out how many jars of jam (which is the number multiplied by 6) and how many packages of bread mix (which is the number multiplied by 5) are in the basket.

Answer 3

b represents the number of breads

8 - b represents the number of jams

5b + 6(8 - b) = 45

Can you solve for b and answer?