Two years ago an egg cost #1 less than last year. this year an egg costs #2 more than last year . the cost of 11 eggs two year ago was the same as the cost of eight eggs this year . what was the cost of an egg last year?
Answers
Let assume that the cost of an egg last year be # x.
So,
- Cost of an egg 2 years ago = # x - 1
and
- Cost of an egg in present year = # x + 2
Hence,
- Cost of 11 eggs 2 years ago = 11(x - 1) = 11x - 11
- Cost of 8 eggs in present year = 8 (x + 2) = 8x + 16
According to statement,
The cost of 11 eggs two year ago was the same as the cost of eight eggs in present year.
⇛ 11x - 11 = 8x + 16
⇛ 11x - 8x = 16 + 11
⇛ 3x = 27
⇛ x = 9
Thus,
- Cost price of an egg in last year = # 9.
Basic Concept Used :-
Writing Systems of Linear Equation from Word Problem.
1. Understand the problem.
- Understand all the words used in stating the problem.
- Understand what you are asked to find.
2. Translate the problem to an equation.
- Assign a variable (or variables) to represent the unknown.
- Clearly state what the variable represents.
3. Carry out the plan and solve the problem.
Given : Two years ago an egg cost 1 less than last year. this year an egg costs 2 more than last year .
the cost of 11 eggs two year ago was the same as the cost of eight eggs this year .
To Find the cost of an egg last year
Solution:
Cost of egg last year = x
Two years ago an egg cost 1 less than last year.
=> Hence cost of egg Two years ago = x - 1
the cost of 11 eggs two year ago = 11 (x - 1)
his year an egg costs 2 more than last year .
=> Hence cost of egg this year = x + 2
cost of eight eggs this year = 8(x + 2)
Equate
11 (x - 1) = 8(x + 2)
=> 11x - 11 = 8x + 16
=> 3x = 27
=> x = 9
cost of an egg last year is 9
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