Answer to Question #262786 in Math for Bjoy

Question

Activity 5.b. Choose a quantity to be represented by a variable, the write a mathematical expression for each.

1. Lota’s age in 5 years

2. a three-digit number whose hundred digits is half the tens digit and the tens digit is 2 more than the units digit.

3. The total interest earned after one year when P100, 000 is invested, part at 6% annual interest rate and the remaining part at 7.5% annual interest rate.

4. The distance traveled by a man driving at the rate of 60 kph

5. The total distance traveled by a boat 1 hour upstream and 30 minutes downstream in which the rate of current is 3kph.

Answer 1

1. Let $x =$ be the present age of Lota. Then the Lota’s age in 5 years will be $(x+5)$ ages.

2. Let $x=$ hundred digit. Then a three-digit number will be

$$100(x)+10(2x)+1(2x+2)$$

$$=100x+20x+2x+2=122x+2, x= 1, 2, 3$$

3. Let $x =$ amount of money invested at 6%, $y =$ amount of money invested at 7.5%.

Given $x+y=100000$

The total interest will be

$$0.06x+0.075y=0.06x+0.075(100000-x)$$

$$=7500-0.015x, 0\leq x\leq100000$$

4. Let $t=$ the time of travel in hours. Then the distance traveled by a man is $60t$ km.

5. Let $v=$ the rate of boat in a steel lake in kph. Then the total distance traveled by a boat is

$$(v-3)\cdot1+(v+3)\cdot0.5=1.5v-1.5, v>3$$