Linear Equations 2 Ques only

2012-03-11 6:52 pm

1.For a two digit number, the ten digit is twice of the units digit. If 18 is subtracted from the number, the result is still a 2-digit number and the new number formed is just the interchanged of the tens and units digit of the original number, find the original 2-digit number.

2. The ingredients needed for baking each tray of cookies and each tray of fruit tarts is tabulated below:

eggs flour

cookies 4 0.48kg

fruit tarts 34 0.36kg

There are 156 eggs and flour 3.84kg to make x trays and y trays, where x and y are positive integers, find the value of x and y to be the most productive.

回答 (1)

用戶2053

2012-03-11 8:43 pm

✔ 最佳答案

1)Let 10x + y be the original 2-digit number , thenThe ten digit is twice of the units digit :x = 2y ..... (1)If 18 is subtracted from the number, the result is still a 2-digit number and the new number formed is just the interchanged of the tens and units digit of the original number :10x + y - 18 = 10y + x ......(2)Substitute (1) into (2) :10(2y) + y - 18 = 10y + 2y
21y - 18 = 12y
9y = 18
y = 2then x = 4 The original 2-digit number is 10*4 + 2 = 42.

2)For eggs to be the most productive :
4x + 34y = 156 ......(1)For flour to be the most productive :
0.48x + 0.36y = 3.84 ......(2)(1) - (2)/0.12 :(4x + 34y) - (4x + 3y) = 156 - 3.84/0.12
31y = 124
y = 4 , put y = 4 to (1) :4x + 34*4 = 156
x = 5

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