► Skill Involving Two or more Quantities With Fixed Total
1) Joshua wanted to tie 45 triangular flags, each with a width of 16 cm, on a rope. He tied the flags 9 cm apart from each other as shown below in the diagram. What was the length of the rope he needed?
Ans :- He needed 1116 cm long rope.
2) The average of 6 numbers is 149. When a 7th number is added, the average of these 7 numbers increases by 2. When an 8th number is added, the average of these 8 numbers is further increased by 2. What is the 8th number?
Ans :- The 8th number is 167
3) 3 girls sold as many Christmas cards as 4 boys. 9 girls and 11 boys sold a total of 483 Christmas cards. How many cards did 10 girls and 17 boys sell?
Ans :- 10 girls and 17 boys sold 637 cards.
4) The total length of 12 ropes and 3 ribbons is 0.252 m shorter than the total length of 3 ropes and 12 ribbons.
(a) What is the difference in length between one piece of rope and one piece of ribbon? (Leave your answer in cm.)
(b) If the length of each piece of rope is 0.53m. what is the length of each piece of ribbon? (Leave your answer in cm.)
Ans :- a) 0.028 cm
b) 0.558 cm
5) An iron rod was 6.47 m long before it was cut into two pieces. The shorter piece was 2.39 m long. The longer one was then cut into 6 equal pieces. Find the length of each of the 6 equal pieces in cm.
Ans :- 68 cm.
6) Jane bought some guppies. She gave away 29 of them. Harry then gave her the same number of guppies as the number of guppies that she had left. In the end, she then put all her guppies equally into 6 bowls. Each bowl contained 14 guppies. How many guppies did Jane buy?
Ans :- Jane bought 71 guppies.
7) 5 friends are playing Wii games on a Friday afternoon from 3 p.m. to 6 p.m. As there were only 4 controllers, they took turns to play. At any time, 3 of them played while the other two watched. If each of them had the same amount of playing time, how many minutes did each of them get to play that afternoon?
Ans :- 108 minutes.
8) There are some apples and pears. If 2 apples are eaten, there will be 3 times as many apples as pears. If 2 pears are eaten, there will be 4 times as many apples as pears. How many apples are there?
Ans :- There are 32 apples.
9) Mr Mohammad bought 26 boxes of erasers. Each box contained an equal number of erasers. After he had given 7 erasers each to 54 children, he had 9 boxes and 13 erasers left. How many erasers were there in each box?
Ans :- There were 23 erasers in each box.
10) At first, there were an equal number of coins in 35 piggy banks. 4 piggy banks were emptied and the coins in them were put equally into the remaining piggy banks. As a result, the number of coins in each remaining piggy bank increased by 16. How many coins were there in the piggy banks altogether?
Ans :- Altogethere there were 4340 coins.
11) A, b and C are 3 numbers. A is ½ the sum of B and C, and B is ¼ the sum of the 3 numbers. Find the ratio of B is to C is to A in its simplest form.
Ans :- 3 : 5 : 4.