Urgently need help. PSLE Math

lein SG

1) Mr Tan bought 3 times as many badges as toycars and spent $144 in total. He spent $84 more on toycars than on badge. Given that a toycar cost $10.40 more than badge, what is the cost of a badge?

ANSWER: $1

2) Mary and Jason each have some money. If mary spent $80/day and Jason spent $40/day, Mary will have $500 left when Jason has spent all his money.

If Mary spends $40/day and Jason spent $80/day, mary will have $1100 left when Jason has spent all his money. What amount of money does Jason have?

ANSWER: $400

voltrons. SG

Q1.

Not sure if you learnt algebra but i'm using it to solve.

Badges : Toy Car

3 : 1

We know he spent $84 more on toycars than on badge.

So 144 - 84 = 60

So Badges cost = 60 / 2 = 30

Amount spend on toy car = 30 + 84 = 114

Let x be the Price of Badge

Let y be the Unit Ratio for Badges and Toy Car

114/y = x + 10.4 equation 1

30/3y = x

10/y = x equation 2

Sub equation 2 into 1

114/y = 10/y + 10.4

114/y = 10/y + 10.4y/y

114 = 10 + 10.4y

114 - 10 = 10.4y

104 = 10.4y

y = 10

Sub y=10 into equation 2

10/10 = x

x = 1

Therefore, the price of a badge cost $1.

voltrons. SG

Q2.

Let x be the no. of days where mary left $500

Let y be the no. of days where mary left $1100

When Mary left $500

Mary spend $80/day --------> 80 x + $500

Jason spend $40/day --------> 40x

When Mary left $1100

Mary spend $40/day ---------> 40y + $1100

Jason Spend $80/day---------> 80 y

40 y + 1100 = 80 x + 500 ----- equation 1

40 x = 80y

x = 2y ------ equation 2

Sub equation 2 into 1

40y + 1100 = 80(2y) + 500

40y + 1100 = 160y + 500

-120y = -600

y = 600/120

y = 5 days

Amount Jason have = 5 days X 80 = $400.

Hope my solution helps. ^^