Question

Can someone walk me through solving this?

Answer 1

I'm so confused

Answer 2

I would, but the wording is a bit confusing..

Answer 3

They're mixing the everyday moisturizing lotion together with the self-tanning lotion to produce an experimental lotion.

Answer 4

Each kind of lotion is measured in ounces.

Answer 5

They give us the amount of ounces for the everyday moisturizing lotion: 300 ounces.

Answer 6

They do not give us the amount of ounces of the other two lotions so we have to create variables for them.

Answer 7

Let us represent the total ounces of self tanning lotion as variable \(s\) and the total ounces of experimental lotion as variable \(e\).

Answer 8

Okay

Answer 9

Then we have the following equation:

\(300 + s = e\)

Answer 10

Next they tell us how much each kind of lotion costs per ounce.

Answer 11

The everyday lotion is worth $0.30 an ounce.
The self tanning lotion is worth $2 an ounce.
The experimental lotion is worth $1.50 an ounce.

Answer 12

We can find the total cost of each lotion. Remember they give us the total ounces of everyday lotion (300 oz), so

$.0.30 \(\times\) 300\) would give us the total cost of everyday lotion.

Answer 13

90? @Hero

Answer 14

We don't have the total amount of ounces of the other kinds of lotions so we have to use the variables to represent the amounts and multiply it by the cost per ounce of each lotion type.

Answer 15

Yes the total cost of the everyday moisturizing lotion is $90

Answer 16

The total amounts for the other lotions we have to write them this way:

The total cost of the self tanning lotion will be represented by
\(2s\)

The total cost of the experimental lotion is represented by \(1.50e\)

Answer 17

This leads us to our next equation where we will combine the total cost of the tanning and mosturizing lotions to get the total cost of the experimental lotion:

\(90 + 2s = 1.50e\)

Answer 18

We now have two equations, one for total ounces and the other for total cost:

Total ounces:
\(300 + s = e\)

Total cost:
\(90 + 2s = 1.50e\)

Answer 19

The two equations together represents a system of equations and we can solve the system for variables \(s\) and \(e\)

Answer 20

@yosoykiara are you still with me?

Answer 21

Would you solve for both equations?

Answer 22

We have to solve them "simultaneously".

Answer 23

But, the thing is, if you notice, in the first equation, we already have an expression for \(e\).

Answer 24

1.50

Answer 25

The expression for \(e\) is \(300 + s\)

Answer 26

We can insert the expression for \(e\) in place of the\(e\) in the second equation.

Answer 27

If we do do this, we will have:
\(90 + 2s = 1.50(300 + s)\).

Answer 28

Now we have an equation in terms of one variable, \(s\).

Answer 29

Which you may be able to solve on your own.

Answer 30

It's going to be 147.96

Answer 31

Please show the work you did to arrive at that amount.

Answer 32

Multiply both sides by 10
10*300+10*2s=10*1.50e
i rewrote the new equation to
20s+3000=40.7742
i put 400.7742 into a decimal which equals 203871/5000
then it will be 20s+3000=203871/500

Answer 33

multiply both sides by 5000
then it will be 100000s+150000000=203871
subtract 150000000 from both sides to get -14796129
then divide 100000/100000=-14796129/100000
s=-14796129/100000
demicial form is: -147.9613