Question

Help with linear equations please!

The student council is having a bake sale. They spend $40 for the ingredients to make brownies and cookies. It costs $1.25 to make a dozen brownies and $1.50 to make a dozen cookies. The brownies sell for $6 per dozen and the cookies sell for $7.50 per dozen. The student council sells a total of $195 in baked goods.

A. Write a system of linear equations with two equations and two variables to represent the situation. What do the variables represent?

B. Use any method to solve the system of linear equations.

Please help !!!

Answer 1

40 = 1.25x + 1.50 y
195 = 6x + 7.50 y
This is true because if the cost is 40 as total, and cost of each brownie is 1.25, while cost of each dozen cookie is 1.50, then we can simply take the basic unit as dozen, and equate it with respect to a variable value x, and y.
The same can be applied to 195, which will give you the x and y in dozens. After which you simply multiply it by 12 to find the numbers.

Answer 2

I don't understand what I have to multiply by 12?

Answer 3

The values of x and y will be in dozens right?
1 dozen of cookies/brownies = 12 cookies/brownies. That would give y ou the exact numerical value. :)

Answer 4

So it would be 33?

Answer 5

or I don't add them?

Answer 6

i get x = 20, y = 10
that is in dozens. :/
I dont understand how you got 33.

Answer 7

First, let's work on your first equation,40=1.25*x+ 1.50* y

This means, see if it can be simplified at all before attempting to solve it.
Multiply x and 1.25

Multiply x and 1


The x just gets copied along.

The answer is x

x

1.25*x evaluates to 1.25x

Multiply y and 1.5

Multiply y and 1


The y just gets copied along.

The answer is y

y

1.50*y evaluates to 1.5y

1.25*x+1.50*y evaluates to 1.25x+1.5y

So, all-in-all, your first equation can be written as: 40 = 1.25x+1.5y

Now, let's work on your second equation,195 =6*x + 7.5*y Multiply x and 6

Multiply x and 1


The x just gets copied along.

The answer is x

x

6*x evaluates to 6x

Multiply y and 7.5

Multiply y and 1


The y just gets copied along.

The answer is y

y

7.5*y evaluates to 7.5y

6*x+7.5*y evaluates to 6x+7.5y

So, all-in-all, your second equation can be written as: 195 = 6x+7.5y

After this initial survey of the equations, the system of equations we'll set out to solve is:
40 = 1.25x+1.5y and 195 = 6x+7.5y
Let's start by solving 40 = 1.25x+1.5y for the variable x.
Move the 40 to the right hand side by subtracting 40 from both sides, like this:
From the left hand side:
40 - 40 = 0

The answer is 0

From the right hand side:
The answer is 1.25x+1.5y-40


Now, the equation reads:
0 = 1.25x+1.5y-40

Move the 1.25x to the left hand side by subtracting 1.25x from both sides, like this:
From the left hand side:
The answer is -1.25x

From the right hand side:
1.25x - 1.25x = 0

The answer is 1.5y-40


Now, the equation reads:
-1.25x = 1.5y-40
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.

The last step is to divide both sides of the equation by -1.25 like this:
To divide x by 1


The x just gets copied along in the numerator.

The answer is x

-1.25x ÷ -1.25 = x

To divide 1.5y-40 by -1.25

divide each term in 1.5y-40 by -1.25 term by term.

To divide y by 1


The y just gets copied along in the numerator.

The answer is y

1.5y ÷ -1.25 = -1.2y


-40 ÷ -1.25 = 32

The solution to your equation is:
x = -1.2y+32

Next, let's solve 195 = 6x+7.5y for the variable y.
Move the 195 to the right hand side by subtracting 195 from both sides, like this:
From the left hand side:
195 - 195 = 0

The answer is 0

From the right hand side:
The answer is 6x+7.5y-195


Now, the equation reads:
0 = 6x+7.5y-195

Move the 7.5y to the left hand side by subtracting 7.5y from both sides, like this:
From the left hand side:
The answer is -7.5y

From the right hand side:
7.5y - 7.5y = 0

The answer is 6x-195


Now, the equation reads:
-7.5y = 6x-195
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.

The last step is to divide both sides of the equation by -7.5 like this:
To divide y by 1


The y just gets copied along in the numerator.

The answer is y

-7.5y ÷ -7.5 = y

To divide 6x-195 by -7.5

divide each term in 6x-195 by -7.5 term by term.

To divide x by 1


The x just gets copied along in the numerator.

The answer is x

6x ÷ -7.5 = -0.8x


-195 ÷ -7.5 = 26

The solution to your equation is:
y = -0.8x+26

Now, plug the earlier result, x=-1.2y+32, in for x everywhere it occurs in
y=-0.8x+26.

This gives y=-0.8(-1.2y+32)+26. Now all we have to do is solve this for y,to have our first solution.
Because of the minus sign
0.8 becomes - 0.8

The answer is -0.8

Multiply y and 1.2

Multiply y and 1


The y just gets copied along.

The answer is y

y

1.2*y evaluates to 1.2y

Because of the minus sign

1.2y becomes - 1.2y

The answer is -1.2y

-1.2*y+32 evaluates to -1.2y+32

Multiply -0.8 by -1.2y+32

we multiply -0.8 by each term in -1.2y+32 term by term.

This is the distributive property of multiplication.

Multiply -0.8 and -1.2y

Multiply 1 and y


The y just gets copied along.

y

-0.8 × -1.2y = 0.96y

Multiply -0.8 and 32


1

-0.8 × 32 = -25.6

-0.8*(-1.2*y+32) evaluates to 0.96y-25.6

-25.6 + 26 = 0.4

The answer is 0.4+0.96y

-0.8*(-1.2*y+32)+26 evaluates to 0.4+0.96y


Move the 0.96y to the left hand side by subtracting 0.96y from both sides, like this:
From the left hand side:
y - 0.96y = 0.04y

The answer is 0.04y

From the right hand side:
0.96y - 0.96y = 0

The answer is 0.4


Now, the equation reads:
0.04y = 0.4
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.

The last step is to divide both sides of the equation by 0.04 like this:
To divide y by 1


The y just gets copied along in the numerator.

The answer is y

0.04y ÷ 0.04 = y


0.4 ÷ 0.04 = 10

The solution to your equation is:
y = 10

Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=-1.2y+32.
This gives x=-1.2(10)+32. Now, simplify this.
Because of the minus sign
1.2 becomes - 1.2

The answer is -1.2

Multiply -1.2 and 10


1

-1.2*(10) evaluates to -12

-1.2*(10)+32 evaluates to 20

x= 20

So, the solutions to your equations are:
x= 20 and y= 10

Answer 8

So basically ur solving by elimination.

Multiply the 1st equation by 5 and the second by -1. And then add the 2 equations.
So

200=6.25x+7.5y
+(-195=-6x-7.5y)
--------------------
5=0.25x
-- -----
0.25. 0.25

X=20

Plug this value of x to one of the original equation to solve for y

Answer 9

I thought I just had to multiply 1.25x12=15 and 1.50x12=18

Answer 10

Can I use my last answer for this next question.

C. What profit did the student council make for the brownies sold? For the cookies sold?

Answer 11

Yes. Multiply the value for dozen by the amount produced, and the amount sold, subtract those quantities to find out the profit made.

Answer 12

I still don't understand.

Answer 13

See. If you have some amount of cookies, and oyu sell them at x, then you will have to multiply the two values to get the amount he earned, and then you will have to subtract it by the cost of production, which is the amount produced multiplied by the price of each dozen of cookie.

Answer 14

Thank you Mathbreaker for your time and consideration :)