SOLUTION: 1) Ben bought five ice-cream cones and received $1.75 change from his $10 note. How much did each ice-cream cone cost? 2) three students take a different routes home from school.

Question 980111: 1) Ben bought five ice-cream cones and received $1.75 change from his $10 note. How much did each ice-cream cone cost?
2) three students take a different routes home from school. Mark needs to walk twice as far as Annette, whereas Sue needs to walk four times as far as Annette. if the three cover a total distance of 2.1km (or 2100m), how far does each need to travel to get home from school?
3) Pete is 7 years older than Sharon and John is twice as old a Peter. Find how old Peter is if the mean (arithmetic average) of their ages is 19.
4) Joseph has 24 cousins. he knows that he has six more females cousins thane male cousins. how amny females cousins does he have?
5) in 3 years' time Joanne will be twice as old as her daughter. If Joanne is 45 years old now, how old is her daughter?
Answer by MR. PICKLES(1) (Show Source): You can put this solution on YOUR website!
1) Ben bought five ice-cream cones and received $1.75 change from his $10 note. How much did each ice-cream cone cost?
let c be the cost of one ice cream cone
10 - 5c = 1.75
10 - 1.75 = 5c
8.75 = 5c
1.65 = c
Therefore, one ice cream cone costs $1.65.
2)Three students take a different routes home from school. Mark needs to walk twice as far as Annette, whereas Sue needs to walk four times as far as Annette. if the three cover a total distance of 2.1km (or 2100m), how far does each need to travel to get home from school?
let:
a be Annette
2a be Mark
4a be Sue
a + 2a + 4a = 2100m
7a = 2100m
a = 300m ------> Annette
2a = 600m -----> Mark
4a = 1200m ----> Sue
3)Pete is 7 years older than Sharon and John is twice as old a Peter. Find how old Peter is if the mean (arithmetic average) of their ages is 19.
let:
s be Sharon's age
7 + s be Pete's age
2(7 + s) be John's age
s + (7 + s) + 2(7 + s) all over 3 = 19
s + 7 + s + 14 + 2s all over 3 = 19
4s + 21 all over 3 = 19
*multiply 3 to 19*, so...
4s + 21 = 57
4s = 57 - 21
4s = 36
s = 9 ----> Sharon's age
7 + s = 19 -----> Pete's / Peter's age
2(7 + s) = 36 --> John's age
4) Joseph has 24 cousins. he knows that he has six more females cousins thane male cousins. how many females cousins does he have?
equation 1 : m + 6 = f
equation 2 : m + f = 24
*substitute equation 1 in equation 2*, so...
m + f = 24 , but f = m + 6 so...
m + m + 6 = 24
2m + 6 = 24
2m = 24 - 6
2m = 18
m = 9
m + 6 = f so, 9 + 6 = 15
Therefore, Joseph has 15 female cousins.
5) let d be daughter's age
let j be Joan's age
3 + j = 2d
3 + 45 = 2d
48 = 2d
24 = d
Therefore, Joan's daughter is 24 years old.

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