Let's assume
number of teaspoons of pure maple syrup=x
now, we can find maple syrup content of pure syrup
so,
maple syrup content of pure syrup=1.00*x
36 tablespoons of a 45% solution
so,
male syrup content of 45% =45% of 36
male syrup content of 45% [tex] =\frac{45}{100} *36 [/tex]
male syrup content of 45% [tex] =0.45*36 [/tex]
so,
total mixture solution =x+36
total maple syrup=60% of (x+36)
and we can also find total maple syrup
total maple syrup =maple syrup content of pure syrup +male syrup content of 45%
total maple syrup [tex] =1.00x+0.45*36 [/tex]
now, we can set it equal
[tex] 0.60(x+36)=1.00x+0.45*36 [/tex]
now, we can solve for x
[tex] 0.60x+0.60*36=1.00x+0.45*36 [/tex]
[tex] 0.60*36-0.45*36=1.00x-0.60x [/tex]
[tex] 0.40x=0.60*36-0.45*36 [/tex]
[tex] 0.40x=0.15*36 [/tex]
[tex] x=13.5 [/tex]
so, 13.5 teaspoons pure maple syrup should be added to 36 tablespoons of a 45% solution in order to obtain a 60% solution..........Answer
