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maths~

2008-03-08 1:52 am

1)A gift shop sells music boxes of two sizes. The price of 4 large and 9 small music boxes is$1275. The price of 7 large and 6 small music boxes is$1500. Mr Wong buys two music boxes of different sizes from the shop. How
much did he pay?
2)The price of a loaf of bread was$5 and that of a can of soft drink was$6.5.
Colin bought altogether 6 of them for$33.
(a)How many loaves of bread and how many cans of soft drink did he buy?
(b)He only had a number of$2-coins and $5-coins at that time. He paid 11 of
them to the shopkeeper and was given a change of$1. How many coins of
each kind did he pay?

*need the step!!

回答 (1)

NCY

2008-03-08 2:55 am

✔ 最佳答案

1)Let x be the price of the big one, Let y be the price of the small one

4x + 9y = 1275 ---(1)

7x + 6y = 1500 ---(2)

(1)2 ﹣(2)3:

8x ﹣21x = 2(1275) ﹣3(1500)

-13x = -1950

13x = 1950

x = 150

Sub it into (1)

4(150) + 9y = 1275

600 + 9y = 1275

9y = 675

y = 75

Therefore, x + y = 150 + 75 = 225

∴Mr Wong need to pay $225

2a)Let x be the loaves of bread and y be the cans of soft drink,
x + y = 6---(1)
5x + 6.5y = 33 ---(2)
From (1),x = 6 ﹣y---(3)
Put (3) into (2),
5(6 ﹣y) + 6.5y = 33
30 ﹣5y + 6.5y = 33
1.5y = 3
y = 2 ---(4)
Put (4) into (3),
x = 6 ﹣2 = 4
∴he bought 4 loaves of bread and 2 cans of soft drink.
b)He has = $33 + $1 = $34 (purchase is 33 and the change is 1).
Let x be the number of $2 coins and y be the number of $5 conins,
2x + 5y = 34 ---(1)
x + y = 11 ---(2)

From (2),x = 11 ﹣y--(3)
Put (3) into (1),
2(11 ﹣y) + 5y = 34
22 ﹣2y + 5y = 34
3y = 12
y = 4 ---(4)
Put (4) into (3),
x = 11 ﹣4 = 7
∴the number of $2 coins is 7 and y be the number of $5 conins is 4.

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