Answer: you will need 14.1 lbs of the cheaper candy 3 lbs of the expensive candy.
Step-by-step explanation:
Let x represent the number of pounds of the cheaper candy that you will need.
Let y represent the number of pounds of the expensive candy that you will need.
You would like to have 17.1 lbs of the candy mixture. It means that
x + y = 17.1- - - - - - - - -1
The mixture would sell for $3.50/lb. It means that the total cos of the mixture would be
17.1 × 3.5 = $59.85
If the cheaper candy sells for $2.50/lb and the expensive candy sells for $8.20/lb, it means that
2.5x + 8.2y = 59.85- - - - - - - - - 1
Substituting x = 17.1 - y into equation 1, it becomes
2.5(17.1 - y) + 8.2y = 59.85
42.75 - 2.5y + 8.2y = 59.85
- 2.5y + 8.2y = 59.85 - 42.75
5.7y = 17.1
y = 17.1/5.7
y = 3
x = 17.1 - y = 17.1 - 3
x = 14.1
Graph of a linear equation will be always straight line.
To obtain desired mixture, we will need 14.1 lbs of the cheaper candy 3 lbs of the expensive candy.
Let us consider x represent the number of pounds of the cheaper candy and y represent the number of pounds of the expensive candy .
We have 17.1 lbs of the candy mixture. It means that
[tex]x + y = 17.1[/tex]
Since, the mixture would sell for $3.50/lb.
Therefore, the total cos of the mixture will be,
[tex]17.1 *3.5 = $59.85[/tex]
If the cheaper candy sells for $2.50/lb and the expensive candy sells for $8.20/lb, Then , equation become
[tex]2.5x + 8.2y = 59.85[/tex]
Substituting [tex]x = 17.1 - y[/tex] into equation [tex]2.5x + 8.2y = 59.85[/tex]
We get, [tex]2.5(17.1 - y) + 8.2y = 59.85[/tex]
[tex]42.75 - 2.5y + 8.2y = 59.85[/tex]
[tex]- 2.5y + 8.2y = 59.85 - 42.75[/tex]
[tex]5.7y = 17.1[/tex]
[tex]y = 3[/tex]
Substituting value of y in equation [tex]x = 17.1 - y[/tex]
[tex]x = 17.1 - y = 17.1 - 3[/tex]
Thus, [tex]x = 14.1[/tex]
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