a%2Bb=12 [1]
.75a%2B1.05b=10.20 [2]
Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):
.75a%2B.75b=9
.75a%2B1.05b=10.2
.3b=1.2
3b=12
b=4
ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.
CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20