Algebra 2 word problem help please?

if you just want to give the answer that is fine, i would definitely appreciate it; but i would love for you to step by step explain to me how you did the problem and got the answer. So i can actually learn how to do this for my test tomorrow!

any help at all is appreciated, thank you!

here is the word problem:

Every month, a girl gets allowence. Assumer last yeat she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she has $7777 left. Assuming she only gets money by allowence, how much money does she earn every month?

Comments

  • Let m be the amount of money (in dollars) that she earned in the past year. Since she spent 1/2 of her money, then 1/3 of that, then 1/4 of that, and is left with $7777, we can write:

    m*1/2*1/3*1/4=7777

    Solving that, we have:

    m*1/24 = 7777

    m = 7777*24

    m = 186648

    So she earned $186648 in the past year.

    Now we need to find out how much she earns per month. Since there are 12 months in a year, we just divide the amount she made in a year by 12. 186648/12=15554, so she earns $15554 per month (which is ridiculous!)

    I hope that helps! Good luck on your test :)

    Edit:

    Why must people waste their time giving thumbs down to correct answers?

  • She spends 1/2 on clothes so has 1/2 left

    She spends 1/3 of that so has 2/3 of that left: 2/3 x 1/2 = 2/6 = 1/3 left

    She spends 1/4 of that so has 3/4 of that left: 3/4 x 1/3 = 3/12 = 1/4 left

    If a 1/4 is left and = $7777 then the whole amount she had originally was 4 x 7777 = $31,108

    (Are these US dollars? If so it sounds like a large amount for a girl's allowance!)

    Did you mean that this is a whole year's allowance?

    If so, the monthly allowance is 31108/12 = $2,592.33

    If you want to do this by an algebraic expression remember that we are dealing with the amount left after each spend - some of the answers here have got this wrong.

    If the proportion spent of the available money at each spend is a, b and c

    Then the amount remaining at the end is given by

    (1 - a)(1 - b)(1 - c)x where x is the riginal amount

    (1 - 1/2)(1 - 1/3)(1 - 1/4)x

    = (1/2 x 2/3 x 3/4)x = (1/4)x

    so (1/4) x = $7777

    x = 4 x $7777 as before

    = $31,108

    = $2,592.33 per month

  • Let the allowance be X. Then you can write equations. Half of her money is spent on clothes, leaving:

    X - ½ X = ½ X

    One third of the remaining money is spent on games, leaving:

    ½ X - (1/3 * ½ X) = 1/3 X (with some work on the fractions)

    ... and so on. Subtract the amount spent in each step from the remaining amount from the previous step. In the end, you get:

    1/3 X - (1/4 * 1/3 X) = $ 7,777

    Solve for X by simplifying the fractions and divide by the resulting coefficient on both sides.

  • You know that she has $7777 left, so you will simply want to work backwards.

    So you will get $7777 and divide by 1/4. Then divide that by 1/3. The finally divide by 1/2.

    That should show you much she had after the end of the year.

    Then you will want to divide by 12 and you will get her allowance per month.

    So her monthly allowance is $15,554

  • x is the primary even quantity x + two is the moment even quantity and x + four would be the 3rd even quantity all of those numbers upload as much as sixty six so x + (x + two) + (x + four) = sixty six 3x + 6 = sixty six 3x = sixty six - 6 3x = 60 x = 60/three x = 20 So the 3 numbers are 20, 22, and 24 M = 4S M = 2S + 20 4S = 2S + 20 2S = 20 S = 10 Son = 10 years as a result Man = forty

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