Help me with these simple math questions please?

1) If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

2) The sales price of a car is $12,590, which is 20% of the original price. What is the original price?

3) Solve the following equation for A: 2A/3= 8+4A

4) If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41, then how old is Sue?

5) Jim is able to sell a hand-carved stone statue for $670 which was 35% profit over his cost. How much did the state originally cost him?

6) Simon arrived at work at 8:15 am and left work at 10:30 pm. If Simon gets paid by the hour at a rate of $10 and time and 1/2 for any hours worked over 8 in a day, how much did Simon get paid?

7) If r = 5 z then 15 z = 3 y, then r =

8) If 300 jellybeans cost you x dollars, how many jellybeans can you purchase for 50 cents at the same rate?

9) If 8x + 5x+2x + 4x =114, then 5x + 3 =

Okay that's all. I can access the answers from the answer key but I still don't understand how to actually solve these questions, so please help with explaining how to do each question rather than just giving the answer. Thanks so much!

2 Answers

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  • 9 years ago
    Favorite Answer

    1)

    Sally does 1/4 of the job per hour, John does 1/6 of the job per hour. Combined, the work at 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the job per hour. Combined they complete the job in 12/5 = 2.4 hours or 2 hours 24 minutes.

    2)

    12,590 = 0.20x

    12590/0.2 = $62,950

    3)

    2A/3 = 8 + 4A

    2A = (8 + 4A)/3

    2A = 8/3 + 4A/3

    2A - 4A/3 = 8/3

    6A/3 - 4A/3 = 8/3

    6A - 4A = 8

    2A = 8

    A = 8/2 = 4

    4)

    a) L = S + 6 or S = L - 6

    b) J = L + 5

    c) L + S + J = 41

    combine eq(a) and (b) into eq(c):

    L + (L - 6) + (L + 5) = 41

    3L - 1 = 41

    3L = 42

    L = 42/3 = 14

    using eq(a):

    S = 14 - 6 = 8

    using eq(b):

    J = 14 + 5 = 19

    check using eq(c):

    14 + 8 + 19 = 41

    Leah is 14 years old, Sue is 8 years old, John is 19 years old.

    5)

    x(1.35) = 670

    x = 670/1.35 = $496.30

    6)

    He worked 14.25 hours, which is:

    8(10) + 6.25(15) = $173.75 for the day

    7)

    a) r = 5z

    b) 15z = 3y or z = 3y/15 = y/5

    substitute eq(b) into eq(a):

    r = 5(y/5) = y

    8)

    300(0.50/x) = n

    9)

    8x + 5x + 2x + 4x = 114

    19x = 114

    x = 114/19 = 6

    5(6) + 3 = 33

    - .--

  • 9 years ago

    1) Sally paints 1/4 house per hour

    John paints 1/6 house per hour

    (1/6 + 1/4)t = 1

    t = 2.4 hours

    4) Let Sue's age be s, John is j, Leah is x

    x = s + 6

    j = x +5

    s + j + x = 41

    (x - 6) + (x + 5) + x = 41

    3x = 42

    x = 14 Leah is 14 years old

    Sue is 14-6 = 8 years old

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