Could someone help me with some math?

Question

I need help with these math problems. I have an exam in a few days and i need someone to explain these practice problems.

1. Roy and Alan share some stamps in the ratio 4:5. the ratio of Roy's US stamps to Australian stamps is 3:5. If Roy has 8 more Australian stamps than US stamps, how many stamps does Alan have?

2. Cindy bought 4 shirts and 3 skirts. the amount of money she spent on all the shirts and all the skirts were in the ratio 10:9. If she bought each skirt at $18, how much did she pay for each shirt?

3. Alvin spends part of his money on food, rent and transport in the ratio of 2:7:5. If he spends 4200 less on transport than on rent, how much money does he spend on these three items?

Answer 1

1. Roy has Australian stamps (call them A) and US stamps (call them U)

A=U+8 (8 more Australian stamps than US stamps)

Since the ratio of US stamps to Australian stamps is 3 to 5 he has 3/5 of a US stamp for every Australian stamp.

A = (3/5)A + 8
(2/5)A = 8
A = 20
U= (3/5)20 = 12

Roy has 32 stamps

Roy has only 4/5th of a stamp for every stamp Alan has, so
Alan has 32/(4/5) = 40 stamps and Roy has 32.

You can try problems 2 and 3.

Answer 2

#1
Ratio of Roy's US to Australian = 3:5 or U:A or U=3A/5.
A = U+8. Subsitute to get A = (3/5)A + 8. Multiple by 5.
5A = 3A + 40. 2A=40 so A=20. U=12.

Roy has 20 Australian and 12 U.S. stamps for a total of 32 stamps. Alan has 5/4 as many stamps as Roy or 40 stamps!

#2
(4 shirts)*($X) = 4X
(3 skirts)*($18) = $54
4X:54 = 10:9 =60:54 so x=$15.
Cindy spent $15 for each shirt!

#3
F:R:T = 2:7:5.
R = 4200 + T. Focus on R:T = 7:5. or R=(7/5*)T

(7/5)*T = 4200 + T. Multiple by 5 again.
7T = 21,000+ 5T or 2T = 21,000. T=$10,500 so rent is $14,700.

14,700:10,500 = 7:5

F = 4200 to get a ratio of 4200:14700 = 2:7

Your totals are 4200+14700 + 10500 or $29,400. Not bad for a bloke.

Answer 3

3.

F – money for food

R – money for rent

T - money for transport

Alvin spends money on food, rent and transport in the ratio of 2:7:5

=>

F/R = 2/7 => 7*F = 2*R => F = (2/7)*R

R/T = 7/5 => 5*R = 7*T => R = (7/5)*T

He spends 4200 less on transport than on rent

=> R = T + 4200

5*( T + 4200) = 7*T

T = (5*4200)/2 = 10500

R = (7/5)*10500 = 14700

F = (2/7)*R = 4200

How much money does he spend on these three items?

4200 for food, 14700 for rent & 10500 for transport.

Try to understand every step & solve the other problems similarly.