A 17 -pound mixture of coffee that contains both decaffeinated and regular coffee costs $ 60. The decaffeinated coffee costs $3 per pound, and the regular coffee costs $4 per pound. (a) Let x be the weight of the decaffeinated coffee and y be the weight of the regular coffee. Write a system of equations whose solution gives the amount of each type of coffee in the mixture.
(b) Use the method of substitution to solve the system of equations.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752