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anonymous

  • one year ago

Can someone walk me through solving this?

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  1. anonymous
    • one year ago
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    I'm so confused

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  2. anonymous
    • one year ago
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    I would, but the wording is a bit confusing..

  3. Hero
    • one year ago
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    They're mixing the everyday moisturizing lotion together with the self-tanning lotion to produce an experimental lotion.

  4. Hero
    • one year ago
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    Each kind of lotion is measured in ounces.

  5. Hero
    • one year ago
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    They give us the amount of ounces for the everyday moisturizing lotion: 300 ounces.

  6. Hero
    • one year ago
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    They do not give us the amount of ounces of the other two lotions so we have to create variables for them.

  7. Hero
    • one year ago
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    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
    • one year ago
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    Okay

  9. Hero
    • one year ago
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    Then we have the following equation: \(300 + s = e\)

  10. Hero
    • one year ago
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    Next they tell us how much each kind of lotion costs per ounce.

  11. Hero
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    90? @Hero

  14. Hero
    • one year ago
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    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
    • one year ago
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    Yes the total cost of the everyday moisturizing lotion is $90

  16. Hero
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    The two equations together represents a system of equations and we can solve the system for variables \(s\) and \(e\)

  20. Hero
    • one year ago
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    @yosoykiara are you still with me?

  21. anonymous
    • one year ago
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    Would you solve for both equations?

  22. Hero
    • one year ago
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    We have to solve them "simultaneously".

  23. Hero
    • one year ago
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    But, the thing is, if you notice, in the first equation, we already have an expression for \(e\).

  24. anonymous
    • one year ago
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    1.50

  25. Hero
    • one year ago
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    The expression for \(e\) is \(300 + s\)

  26. Hero
    • one year ago
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    We can insert the expression for \(e\) in place of the\(e\) in the second equation.

  27. Hero
    • one year ago
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    If we do do this, we will have: \(90 + 2s = 1.50(300 + s)\).

  28. Hero
    • one year ago
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    Now we have an equation in terms of one variable, \(s\).

  29. Hero
    • one year ago
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    Which you may be able to solve on your own.

  30. anonymous
    • one year ago
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    It's going to be 147.96

  31. Hero
    • one year ago
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    Please show the work you did to arrive at that amount.

  32. anonymous
    • one year ago
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    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
    • one year ago
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    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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spraguer (Moderator)
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