Question

Plss help!!

1. Abigail is 8 years older than Cynthia. Twenty years ago Abigail was three times as old as Cynthia. How old is each now?

2. Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.

3. Bill is 5 years older than Sue is, and the sum of their ages is 67 years. How old is Bill and Sue?

4. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digits, and the tens digit equals to the sum of the other two. Find the number.

5. The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.

Answer 1

1. a = 32, c = 24

Explanation:

a = c+8

a-20 = 3(c-20)

(c+8)-20 = 3c-60

c = 24

a = 24+8

a = 32

2. t = 15, j = 9

t-3 = 2(j-3)

t-3 = 2j-6

t = 2j-3

t + 2 + j + 2 = 28

(2j-3)+ 2 + j + 2 = 28

3j + 1 = 28

3j = 27

j = 9

t-3 = 2(9-3)

t-3 = 2(6)

t-3=12

t = 15

3. b=36, s=31

b = s + 5

b+s = 67

(s+5)+s = 67

2s+5 = 67

2s = 62

s = 31

b = 31+5

b = 36

4. 231

h + t + u = 6

(with h=hundreds digit, t=tens digit, u=units digit)

h = 2u

t = h+u

t = (2u) + u

(2u) + (2u +u) + u = 6

6u = 6

u = 1

h = 2

t = 3

the number is 231

5. 48

u = 2t

the 2-digit number is 10t+u

2(10t+u) = 10u+t+12

2(10t + 2t) = 10(2t) + t + 12

20t + 4t = 20t + t + 12

24t = 21t + 12

3t = 12

t = 4

u = 2*4

u = 8

the number is 48