Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 magazines, he would have run short of $4.
A student concluded that the price of each CD is $5 and the price of each magazine is $6. Which statement best justifies whether the student's conclusion is correct or incorrect? (4 points)
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (9, 4).
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (5, 6).
Answers
Given : Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 magazines, he would have run short of $4.
A student concluded that the price of each CD is $5 and the price of each magazine is $6.
To Find : Which statement best justifies whether the student's conclusion is correct or incorrect?
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (9, 4).
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (5, 6).
Solution:
4x + 2y = 32
5x + 2y = 36
=> x = 4
=> 4(4) + 2y = 32
=> 2y = 16
=> y = 8
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
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