Can you please help with this problem:
At Super Saver Mart (SSM), you can buy three packs of toilet paper and seven boxes of cereal for $46.00. You can also purchase 8 packs of toilet paper and 4 boxes of cereal for $75.00 at SSM. What is $14 more than the combined price of one pack of toilet paper and one box of cereal? Write a system of equations for this situation and find its solution.
This is what I have so far:
3x + 7y = $46.00
8y + 4y = $75.00
7y = 46.00 + 3x
I am not sure what my next step would be...please help
First of all , define your variables
3x + 7y = $46.00
8x + 4y = $75.00 <----- notice correction
3x + 7y = $46.00 (times 8): 24x + 56y = 368
8x + 4y = $75.00 (times 3): 24x + 12y = 225
subtract them:
44y = 143
y = 3.25
go back into one of the original equations to find x, then follow the instructions.
To solve this problem, let's write a system of equations to represent the situation at Super Saver Mart.
Let's use the variables x to represent the price of one pack of toilet paper and y to represent the price of one box of cereal.
From the information given, we can set up the following two equations:
Equation 1: 3x + 7y = 46.00 (Three packs of toilet paper and seven boxes of cereal cost $46.00)
Equation 2: 8x + 4y = 75.00 (Eight packs of toilet paper and four boxes of cereal cost $75.00)
Now, let's solve the system of equations by using the method of substitution:
Step 1: Solve Equation 1 for x in terms of y:
From Equation 1, we have: 3x = 46.00 - 7y
Dividing both sides by 3, we get: x = (46.00 - 7y)/3
Step 2: Substitute the expression for x into Equation 2:
Substituting (46.00 - 7y)/3 for x in Equation 2, we get:
8(46.00 - 7y)/3 + 4y = 75.00
Step 3: Simplify and solve for y:
Multiplying through by 3 to eliminate the fraction, we get:
8(46.00 - 7y) + 12y = 225.00
368.00 - 56y + 12y = 225.00
Combining like terms, we have:
-44y = -143.00
Dividing both sides by -44, we find:
y = 143.00/44
Simplifying, this gives us:
y ≈ 3.25
Step 4: Substitute the value of y back into Equation 1 to find x:
3x + 7(3.25) = 46.00
3x + 22.75 = 46.00
3x = 46.00 - 22.75
3x = 23.25
Dividing both sides by 3, we find:
x ≈ 7.75
So, the price of one pack of toilet paper (x) is approximately $7.75 and the price of one box of cereal (y) is approximately $3.25.
Now, to find the combined price of one pack of toilet paper and one box of cereal, we can simply add x and y:
Combined price = x + y
Combined price ≈ 7.75 + 3.25
Combined price ≈ 11.00
Finally, we need to determine what is $14 more than the combined price:
$14 more than the combined price = Combined price + $14
$14 more than the combined price ≈ 11.00 + 14.00
$14 more than the combined price ≈ $25.00
Therefore, $14 more than the combined price of one pack of toilet paper and one box of cereal is $25.00.
So, the solution to the system of equations and the answer to the problem is $25.00.