Question 130899
Let t=income from teaching, p=income from painting, b=income from book sales.
t=p+6000
b=(t+p)/7
b+t+p=48000
(t+p)/7 +p+6000+p=48000 substitute
(p+6000+p)/7 + p+6000 + p = 48000 more substitution
(2p+6000)/7 + p+6000 + p = 48000
(2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.
2p+6000+7p+42000+7p=336000
16p+48000=336000
16p=336000-48000
16p=288000
16p/16=288000/16
p=$18,000.
.
t=18000+6000
t=$24,000.
.
b=(24000+18000)/7
=42000/7
=$6000.
.
Ed