EXAMPLES
Ex 1:
3 girls go to the theatre. The cost of the ticket and popcorn is Rs.30 and Rs.20 respectively. What is the total cost of the ticket and popcorn for 3 girls?
Sol:
Let x = cost of ticket per person
y = cost of popcorn per person
Total cost of the movie (ticket + popcorn) per person = x + y
| Total cost of ticket + popcorn for 3 girls | = | 3(x + y) |
| = | 3(30 + 20) | |
| = | 3(50) | |
| = | 150 |
Ex 2:
Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction and multiplication:
(i) 3 times x added to y.
(ii) 4 times the sum of x and y.
(iii) 3 times x is subtracted from y.
Sol:
(i) 3x + y
(ii) 4(x + y)
(iii) y – 3x
Ex 3:
Write each of the following phrases by using numbers, literals and signs of basic operations:
(i) Quotient of z by 6 is multiplied by y.
(ii) Quotient of x by y added to the product of x and y.
(iii) 3 taken away from the quotient of x by 2y.
(iv) Eight times a number p is x less than a number y.
Sol:
(i) We have,
The quotient of z by 6 = 
∴ The quotient of z by 6 is multiplied by y means, × y = 
.
× y = .(ii) We have,
The quotient of x by y = 
, and the product of x and y = xy.
, and the product of x and y = xy.∴ The quotient of x by y is added to the product of x and y = + xy.
+ xy.(iii) We have,
The quotient of x by 2y = 
.
.∴ 3 taken away from the quotient of x by 2y = – 3.
– 3.(iv) We have,
8 times a number p = 8p.
x less than a number y = y – x.
∴ Eight times a number p is x less than a number y means
8p = y – x.
Ex 4:
The score of Siri in Mathematics is 25 more than two third of her score in Science. If she scored x marks in Science, determine her score in Mathematics.
Sol:
We have,
Score in Science = x
⇒ Two third score in Science = 
x
x ∴ 25 more than two third of score in Science = x + 25
x + 25Hence, the score in Mathematics = x + 25.
x + 25.
Ex 5:
Ravi starts from Delhi at 8 AM to Jaipur. If his car is running at the speed of x km/hr and 1 PM he observes that he is 20 km away from Jaipur. Find the distance between Delhi and Jaipur.
Sol:
| We have | ||
| Total time for 8 A.M to 1 P.M | = | 5 hours |
| Ravi's car is running at the rate of x km/hr. | ||
| ∴ Distance travelled by it in 5 hours | = | (5 times x) km |
| = | 5x km [Distance = Speed × Time] |
At 1 PM.,i.e.,after 5 hours Ravi is still 20 km away from Jaipur
| ∴ Distance between Delhi and Jaipur | = | (20 km more than 5x) km |
| = | 5x + 20 km |