SOLUTION: (Algebra) A family allows 1/3 of its income for housing and 1/4 of its income for food. It budgets a total of $1050 a month for housing and food. What is the family's monthly in

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Question 997622: (Algebra)
A family allows 1/3 of its income for housing and 1/4 of its income for food. It budgets a total of $1050 a month for housing and food. What is the family's monthly income?
Answer by MathLover1(20849) About Me  (Show Source):
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let income be x
if a family allows 1%2F3 of its income for housing and 1%2F4 of its income for food, means x%2F3 of its income for housing and x%2F4 of its income for food
if it budgets a total of $1050 a month for housing and food,means
x%2F3%2Bx%2F4=1050....solve for x
x%2F3%2Bx%2F4=1050...find common denominator; for 3 and 4 will be 12
4x%2F%284%2A3%29%2B3x%2F%283%2A4%29=1050

4x%2F12%2B3x%2F12=1050
%284x%2B3x%29%2F12=1050
7x%2F12=1050
7x=1050%2A12
x=12600%2F7
highlight%28x=1800%29
so,the family's monthly income is $1800
check:
$x%2F3=1800%2F3=600 of its income for housing, and
$x%2F4=1800%2F4=450 of its income for food
$600%2B450=1050 which verifies our answer