You can use those variables specified to make symbolic relation between the cost and number of items. Then you can use any of the methods to solve the obtained system of equations.
The cost of items from shelf A is x = $6
The cost of items from shelf B is y = $4
Given that:
- You can purchase 3 items from shelf A and 2 from shelf B for $26, or
- You can purchase 2 items from shelf A and 5 from shelf B for $32.
x represents the cost of an item from shelf A
y represents the cost of an item from shelf B
How to form the symbolic relation or equation between the cost and the number of items picked from each shelf?
From given data, we have:
[tex]3 \times x + 2 \times y = \$26\\
2 \times x + 5 \times y = \$32[/tex]
Or, we get the system of equations as:
[tex]3x + 2y =26\\
2x + 5y = 32[/tex]
Using the method of substitution to deduce the solution:
[tex]3x + 2y = 26\\
2y = 26 - 3x\\
y = \dfrac{26-3x}{2} = 13 - 1.5x[/tex]
Substituting this value of y in second equation, we get:
[tex]2x + 5y = 32\\
2x + 5(13-1.5x) = 32\\
2x - 7.5x + 65 = 32\\
-5.5x = -65 + 32\\
5.5x = 33\\\\
x = \dfrac{33}{5.5}\\\\
x = 6[/tex]
Using this value of x, we get:
[tex]y = 13 - 1.5x\\
y =13 - 1.5 \times 6\\
y = 13 - 9 = 4[/tex]
Thus, we have:
The cost of items from shelf A is x = $6
The cost of items from shelf B is y = $4
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