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Sagot :
Answer:
6 pounds of strawberry
6 pounds of pineapples
Explanation:
Let,
s = number of pounds of strawberry
p = number of pounds of pineapples
Now we are told that Malcolm is making 12 pounds of fruit salad with pineapple and strawberries. This means
[tex]s+p=12[/tex]Furthermore, we are also told that Pineapples cost $7.50 per pound and strawberries cost $10.50 per pound. This means that the cost of the mixture will be
[tex]7.50p+10.50s[/tex]Therefore, the cost per pound of the mixture is
[tex]\frac{7.50p+10.50s}{12}[/tex]which we are told is $9 per pound. Therefore,
[tex]\frac{7.50p+10.50s}{12}=9[/tex]We can multiply both sides of the above equation by 12 and get:
[tex]7.50p+10.50s=9\times12[/tex][tex]7.50p+10.50s=108[/tex]Hence, we have two equations and two unknowns:
[tex]\begin{gathered} p+s=12 \\ 7.50p+10.50s=108 \end{gathered}[/tex]To solve the above system for s and p, we first solve for p in the first equation.
Subtracting s from both sides of the first equation gives
[tex]\begin{gathered} p+s=12 \\ \Rightarrow p=12-s \end{gathered}[/tex]Substituting this value of p in the second equation gives
[tex]7.50(12-s)+10.50s=108[/tex]which we expand to get
[tex]90-7.50s+10.50s=108[/tex][tex]90+3s=108[/tex]Subtracting 90 from both sides gives
[tex]3s=108-90[/tex][tex]3s=18[/tex]Finally, dividing both sides by 3 gives
[tex]s=18/3[/tex][tex]\boxed{s=6.}[/tex]WIth the value of s in hand, we now find p.
[tex]p+s=12[/tex]Putting s = 6 into the above equation gives
[tex]p+6=12[/tex]subtracting 6 from both sides gives
[tex]\boxed{p=6.}[/tex]Hence, s = 6 and p = 6. This means, 6 pounds of strawberry and 6
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