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## anonymous one year ago Can someone walk me through solving this?

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1. anonymous

I'm so confused

2. anonymous

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

3. Hero

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

4. Hero

Each kind of lotion is measured in ounces.

5. Hero

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

6. Hero

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

7. Hero

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

8. anonymous

Okay

9. Hero

Then we have the following equation: $$300 + s = e$$

10. Hero

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

11. Hero

The everyday lotion is worth $0.30 an ounce. The self tanning lotion is worth$2 an ounce. The experimental lotion is worth $1.50 an ounce. 12. Hero We can find the total cost of each lotion. Remember they give us the total ounces of everyday lotion (300 oz), so$.0.30 $$\times$$ 300\) would give us the total cost of everyday lotion.

13. anonymous

90? @Hero

14. Hero

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.

15. Hero

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

16. Hero

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 $$1.50e$$

17. Hero

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: $$90 + 2s = 1.50e$$

18. Hero

We now have two equations, one for total ounces and the other for total cost: Total ounces: $$300 + s = e$$ Total cost: $$90 + 2s = 1.50e$$

19. Hero

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

20. Hero

@yosoykiara are you still with me?

21. anonymous

Would you solve for both equations?

22. Hero

We have to solve them "simultaneously".

23. Hero

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

24. anonymous

1.50

25. Hero

The expression for $$e$$ is $$300 + s$$

26. Hero

We can insert the expression for $$e$$ in place of the$$e$$ in the second equation.

27. Hero

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

28. Hero

Now we have an equation in terms of one variable, $$s$$.

29. Hero

Which you may be able to solve on your own.

30. anonymous

It's going to be 147.96

31. Hero

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

32. anonymous

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

33. anonymous

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

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