As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor shou
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Answer:
The cost of each pens is $1.19
The cost of each pencils is $0.39
Step-by-step explanation:
Given as :
The number of pens bought by Gabby = 4
The number of pencils bought by Gabby = 5
The number of pens bought by Sydney = 5
The number of pencils bought by Sydney = 3
The total cost of Gabby items = $6.71
The total cost of Sydney items =$7.12
Let The cost of each pens = x
And The cost of each pencils = y
Now, According to question
For Gabby
4 x + 5 y = $6.71 .............1
For Sydney
5 x + 3 y = $7.12 .............2
Now, Solving both equations
5 × (4 x + 5 y) - 4 × (5 x + 3 y) = 5 × 6.71 - 4 × 7.12
Or, 20 x + 25 y - 20 x - 12 y = 33.55 - 28.48
Or, (20 x - 20 x) + (25 y - 12 y) = 5.07
or, 0 + 13 y = 5.07
∴ y =
I.e y = $0.39
So, The cost of each pencils = y = $0.39
Again , put The value of y in eq 1
I,e 4 x + 5 y = $6.71
Or, 4 x + 5 × 0.39 = 6.71
or, 4 x + 1.95 = 6.71
or, 4 x = 6.71 - 1.95
or , 4 x = 4.76
∴ x =
I.e x = $1.19
The cost of each pens = x = $1.19
Hence The cost of each pens is $1.19
And The cost of each pencils is $0.39 Answer