Question

Sally is going to buy a total of 11 new items at target. she is going to buy jeans, dresses, and shoes. she is going to spend exactly $460 and has discovered that jeans are $25, dresses are $50, and shoes are $40. she is also going to buy twice as many shoes as jeans. find out how many jeans, how many shoes, and how many dresses she will buy?

Answer 1

By setting up a system of equations with the given information, we can determine that Sally will buy 2 jeans, 4 shoes, and 5 dresses with her $460 at Target.

Step-by-step explanation:

To solve for the number of jeans, shoes, and dresses Sally will buy, we can set up a system of equations to represent the situation.

Step 1: Establish Variables and Equations

Let's define our variables:

• Jeans: J
• Shoes: S
• Dresses: D

From the information given, we have the following equations:

1. J + S + D = 11 (total items)
2. 25J + 50D + 40S = 460 (total cost)
3. S = 2J (twice as many shoes as jeans)

Step 2: Solve the Equations

Using the third equation, we can replace S in the other equations with 2J:

• J + 2J + D = 11 => 3J + D = 11
• 25J + 40(2J) + 50D = 460 => 105J + 50D = 460

Now we have two equations and two variables (J and D):

• 3J + D = 11
• 105J + 50D = 460

By multiplying the first equation by 50 to get the coefficients of D to match, we have:

• 150J + 50D = 550

Subtracting this from the second equation gives us:

• (105J + 50D) - (150J + 50D) = 460 - 550
• -45J = -90
• J = 2

Plugging J back into the first equation, we get:

• 3(2) + D = 11
• 6 + D = 11
• D = 5

Now we know J and D, so we can find S:

• S = 2J
• S = 2(2)
• S = 4

Step 3: Answer the Question

Sally will buy 2 jeans, 4 shoes, and 5 dresses.