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Sagot :
Given:
Type A
- cost: $5.35 per pound
Type B
-cost: $4.10 per pound
Uses twice as many pounds of type B as type A: B = 2A
Total cost - $487.80
Find: the number of pounds of Type A coffee used
Solution:
Let a = number of pounds used for Type A coffee
Let b = number of pounds used for Type B coffee
We know that the total cost for both coffee is $487.80 so, we can write equation 1:
[tex]5.35a+4.10b=487.80[/tex]We also know that this month's blend used twice as many pounds of type B coffee as type A. This means b = 2a. So, we can replace "b" in equation 1 with "2a". So, the equation 1 becomes:
[tex]5.35a+4.10(2a)=487.80[/tex][tex]5.35a+8.2a=487.80[/tex]To solve for a, first, add similar terms 5.35a and 8.2a.
[tex]13.55a=487.80[/tex]Then, divide both sides of the equation by 13.55.
[tex]\frac{13.55a}{13.55}=\frac{487.80}{13.55}[/tex][tex]a=36[/tex]Therefore, 36 pounds of Type A coffee were used during this month.
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