Maths Problems 1 October 09

1. Elaine’s mom gave her money to buy some markers of the same price.
If she bought 8 such markers, she would have $8 left over.
If she bought 12 such markers, she would have $6 short.

(a) How much money did Elaine’s mom give her?
(b) How many markers could she buy if her mom were to give her another $14?

2.
A librarian counted the number of adults in the library and found that 2/5 of the number of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2.

(a) What was the ratio of the number of women at first to the number of men at first? Give your answer in its simplest form.
(b) Find the number of women in the library at first.

3.
Cinema admission tickets for children were priced at $8 each. There were 20 more boys than girls in the cinema for the first movie. For the second movie, the number of boys decreased by 10% but the number of girls increased by 5%. If there were 408 children at the second movie, how much money was collected from the sales of admission tickets for the first movie?

4.
A van travelled from Town A to Town B at an average speed of 55 km/h. A car started its journey from Town B to Town A at the same time as the van, travelling at an average speed of 90 km/h. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns.

5. At first, 25% of Kumar’s money was the same as 33 1/3% of Lily’s money.
Lily’s father gave her $80 later, while Kumar spent $325.
In the end, Lily had 2 1/2 times as much money as Kumar.
(a) How much money did Kumar have at first?
(b) How much money did Lily have in the end?