Need heLp in word problems..?

Question

How to solve this problems?

a.find three consecutive integers whose sum is 75.

b.A man is 42 years old and his son is 12.In how many years will father be twice as old as his son?

c.How much 20%hydrochloric acid must be mixed with 40ml of 8% acid to form the 12% acid that is needed in an experiment.

Answer 1

a.find three consecutive integers whose sum is 75.

Let:

1st integer = x

2nd integer = x + 1

3rd integer = x + 2

Then:

x + (x+1) + (x + 2) = 75

x + x +1 + x + 2 = 75

3x + 3 = 75

3x = 72

x = 24

and

x + 1 = 25

x + 2 = 26

The answer is 24, 25, 26

b.A man is 42 years old and his son is 12.In how many years will father be twice as old as his son?

Let:

x = number of years until father is twice as old as son

42 + x = age of father in x years

12 + x = age of son in x years

Then:

42 + x = 2(12 + x)

42 + x = 24 + 2x

42 = 24 + x

x = 18

In 18 years the father will be 60 and the son will be 30.

c.How much 20%hydrochloric acid must be mixed with 40ml of 8% acid to form the 12% acid that is needed in an experiment.

Given:

Amount of acid in 40ml of 8% solution = .08 x 40ml = 3.2 ml

Let:

x = amount of 20% acid to add

0.2x = amount of acid in 20% solution = 0.2x

40ml + x = total amount of combined solution

D = desired amount of acid in combined solution = 0.12 * (40 + x)

T= total acid in combined solution = 3.2 + 0.2x

Then, set desired amount of acid in combined solution (D) equal to total acid in combined solution (T):

0.12 * (40 + x) = 3.2 + 0.2x

4.8 + .12x = 3.2 + .2x

4.8 = 3.2 + .08x

1.6 = .08x

x = 1.6 / .08 = 20

You must add 20ml of 20% acid to the 40ml of 8% acid to make a 12% acid solution.

Answer 2

a. Call one integer x. In this case, the smallest is most convenient. Determine what the other integers are in relationship to x. As x is smallest, these are x+1 and x+2. Add all three together, combining like terms, and set to equal 75. Solve for x, then plug back in to expressions for integers.

smallest integer: x=72                      x+x+1+x+1+1=75

next integer: x+1=72+1=73               (x+x+x)+(1+1+1)=75

largest integer: x+1+1=72+2=74                         3x+3=75

                                                                           - 3  - 3

                                                                       --------------

                                                                           3x=72

                                                                   div.by3   div.by3

                                                                          -----------

                                                                               x=72

b. Find the difference between the two ages. The man will be twice his son's age when the son's age is equal to this number. Subtract the father's current age from the age he will be then, or the son's current age from the age he will be then.

42        30        60        30          Answer: 18 years

-12       X2       -42       -12

-----     ------      ------      ------

30       60        18         18

c. You make a table. I need to sleep, so if you don't get this from anyone else I'll come back during the day.