# 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!

Relevance

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

- .--

• 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