Helen and Maggie are going to the store to purchase snack sized bags of chips and bags of pretzels for the baseball team. Helen purchased 20 bags of chips and 10 bags of pretzels and spent $10. Maggie purchased 15 bags of chips and 15 bags of pretzels and spent $11.25. How much is a snack sized bag of chips and a snack sized bag of pretzels? Create and solve a system of equations to solve the problem(Identify what your variables represent). Write a sentence stating the solution.

Question

Helen and Maggie are going to the store to purchase snack sized bags of chips and bags of pretzels for the baseball team. Helen purchased 20 bags of chips and 10 bags of pretzels and spent $10. Maggie purchased 15 bags of chips and 15 bags of pretzels and spent $11.25. How much is a snack sized bag of chips and a snack sized bag of pretzels? Create and solve a system of equations to solve the problem(Identify what your variables represent). Write a sentence stating the solution.

Could someone help me pls.

Answer 1

20c + 10p = 10

15c + 15p = 11.25
Multiply first equation by 3.
60c + 30p = 30
Multiply second equation by 2
30c + 30p = 22.5
Subtract equation 2 from equation 1.
30c = 7.5
Solve for c, then p.

Answer 2

Sure! Let's start by assigning variables to the unknown quantities we need to find.

Let's say a snack-sized bag of chips costs $x and a snack-sized bag of pretzels costs $y.

Now, let's set up a system of equations based on the information given.

Equation 1: Helen purchased 20 bags of chips and 10 bags of pretzels, spending $10.
This can be represented as 20x + 10y = 10.

Equation 2: Maggie purchased 15 bags of chips and 15 bags of pretzels, spending $11.25.
This can be represented as 15x + 15y = 11.25.

We now have a system of equations:
20x + 10y = 10
15x + 15y = 11.25

To solve this system, we can use a method such as substitution or elimination. Let's use the elimination method.

First, let's multiply Equation 2 by 2 to make the coefficients of x in both equations equal:
30x + 30y = 22.5

Now, subtract Equation 1 from the modified Equation 2:
(30x + 30y) - (20x + 10y) = 22.5 - 10
10x + 20y = 12.5

Now, we have two equations:
20x + 10y = 10
10x + 20y = 12.5

Next, let's multiply Equation 1 by 2 to make the coefficients of y in both equations equal:
40x + 20y = 20

Subtract Equation 2 from the modified Equation 1:
(40x + 20y) - (10x + 20y) = 20 - 12.5
30x = 7.5
x = 7.5/30
x = 0.25

Now, substitute the value of x into one of the original equations, let's use Equation 1:
20(0.25) + 10y = 10
5 + 10y = 10
10y = 10 - 5
10y = 5
y = 5/10
y = 0.5

So the solution to the system of equations is x = 0.25 and y = 0.5.

Therefore, a snack-sized bag of chips costs $0.25 and a snack-sized bag of pretzels costs $0.5.

20c + 10p = 10

thank you

Sure! Let's start by assigning variables to the unknown quantities we need to find.