I am lost and need some help with this problem. A grocer needs to mix raisins at

Question

I am lost and need some help with this problem. A grocer needs to mix raisins at $2.00 per pound with granolaat $3.35 per pound to obtain 10 pounds of a mixture that costs$2.50 per pound. How many pounds of raisins and how manypounds of granola must be used? Please show how you arrive at your answer. I am lost and need some help with this problem. A grocer needs to mix raisins at $2.00 per pound with granolaat $3.35 per pound to obtain 10 pounds of a mixture that costs$2.50 per pound. How many pounds of raisins and how manypounds of granola must be used? Please show how you arrive at your answer.

Explanation / Answer

To solve this problem you can use a sysyem of equations. This problem has 2 variables and therefore requires 2equations. If we let R = the lbs of raisins and G = lbs of Granola thenwe have: R + G = 10     and 2.00R + 3.35G = 25.00    (10lbs X $2.50 perlb.) Now we can solve the first equation for one variable: G= 10 - R     (or you could use R = 10 -G) Now replace G in the second equation with (10 - R) and weobtain: 2.00R + 3.35 (10 - R) = 25.00    (now that theequation contains only one variable it can easily be solved) 2.00R + 33.50 - 3.35R = 25.00 -1.35R = -8.50 R= 6.2963 Now we can plug R back into either equation and solve forG. (6.2963) + G = 10 G = 3.7037 So 6.2963 lbs. of Raisins and 3.7037 lbs. of Granola need tobe used.

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