Answer to Question #319375 in Mechanical Engineering for Yanah

Question

Choose a quantity to be represented by a variable, then write a mathematical expression for each.

1. The product of three consecutive integers

2.. Jose's age in 10 years

3. The distance traveled by a man driving at the rate of 45 kph

4. The total amount in pesos of 30 coins consisting of 5-peso coins and 10-peso coins

5. The sum of three consecutive odd integers

6. The fraction of work done by a man who can finish a job in three days

7. The total interest after one year if a fraction of P500 000 is invested at 5% annual interest rate and the remaining part is invested at 7.5% annual interest rate

8. A three-digit number whose hundreds digit is twice its tens digit and the tens digit is 3 more than the units digit

9. The percentage of alcohol in a mixture formed by combining 1.5 liter of pure water and x liters of 30% alcohol solution.

10. The total distance traveled by a boat 1 hour and 20 minutes upstream and 40 minutes downstream if the rate of the current is 3 kph.

Answer 1

1. Let first integer be x

Answer = x+(x+1)+(x+2)

2. Let Jose's current age be y

Answer = y+10

3. Let time he has travelled be t

Distance = speed * time

Answer = 45t

4. Let 5 peso coins be s and 10 peso coins be x

Answer;

30 = 5s + 10x

5. Let first off integer be x

Answer = x+(x+2)+(x+4)

6. Let x be amount of work done

Answer = $\frac{x}{3}$

7. Let x be fraction invested at 5%

Answer = 0.05x + 0.75(500000-x)

8. Let the ones digit be c, the tens digit be b and the hundreds digit be a

Answer = (2b)(c+3)(c)

9. Answer = $\frac{0.3x}{1.5+x}$

10. Distance = speed*time

=3*1.3+3*0.67

=6km