Question

Solve the following problems first using a tape diagram and then by setting up an equation. For each, give your opinion on which solution method was easier. Can you see the connection(s) between the two methods? What does each "unit" in the tape diagram stand for?

a. 16 years from now, Pia’s age will be twice her age 12 years ago. Find her present age.
b. The total age of a woman and her son is 51 years. Three years ago, the woman was eight times as old as her son. How old is her son now?
c. Five years from now, the sum of the ages of a woman and her daughter will be 40 years. The difference in their present age is 24 years. How old is her daughter now?
d. Find three consecutive integers such that their sum is 51.

Answer 1

a. Pia´s age is 40.

b. The age of the woman is 43 and the age of the son is 8

c. The age of the woman is 27 and the age of the daughter is 3.

d. The consecutive integers are 16, 17 and 18.

Explanation:

You can solve these problems using easiest formulas thus.

a. Where Pia's age is X, could be expressed as: X + 16 That is the same than 2×(X-12). Thus:

X+16 = 2×(X-12)

X+16 = 2X-24

40 = X. Thus, Pia´s age is 40

b. The age of the woman is X and the age of the son is Y. Thus, X + Y = 51. Three years ago, the woman was eight times as old as her son. That means: X-3 = 8×(Y-3)

X+Y = 51; X = 51-Y

X-3 = 8×(Y-3)

X - 3 = 8Y - 24

8Y - 24 = (51 - Y) - 3

9Y = 72

Y = 8

X = 51- 8 = 43.

The age of the woman is 43 and the age of the son is 8.

c. The age of the Woman is X and the age of the Daughter is Y. In five years. X + Y = 40, that's the same than X+5 + Y+5 = 40. X - Y = 24.

Thus

X + Y = 30; Y = 30-X

X - Y = 24

X - (30-X) = 24

2X = 54

X = 27

27 - 24 = 3 = Y.

The age of the woman is 27 and the age of the daughter is 3.

d. Five three consecutives integers that sum 51 means.

X + (X+1) + (X+2) = 51

3X + 3 = 51

3X = 48

X = 16

X+1 = 17

X+2 = 18

The consecutive integers are 16, 17 and 18

I hope it helps!