# incomeSomeone's income is 7200 a month. The person plans to budget (1/3) of his income for rent and (1/5) of his income for electricity. What fraction of his income does he plan to spend on...

income

Someone's income is 7200 a month. The person plans to budget (1/3) of his income for rent and (1/5) of his income for electricity. What fraction of his income does he plan to spend on these two items together?

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that the total income is 7200 a month.

The person plans to spend (1/3) of his income for rent.

Then we will assume that the cost of the rent is x.

Then x = (1/3) * total income

==> x = (1/3) * 7200 = 7200 / 3 = 2400

Then he will spend 2400 for rent.

Also, the person is planning on spending 1/5 of his income on electricity.

Let y be the cost of electricity.

==> y= (1/5) * 7200 = 7200 / 5 = 1440

Now we will calculate the total cost of both items.

==> x + y = 2400 + 1440 = 3840.

Then he will spend 3850 of his total income of 7200 on those items.

==> Then let the fraction of both items be z.

==> z * 7200 = 3840

==> z = 3840 / 7200 =  8 / 15.

Then the fraction is 8/15 of his income we will be spent on both items.

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

One way to do this is to find a way to get these fractions to have the same denominator.  In this case, that you could be 15.  So 1/3 (for rent) is the same as 5/15.  1/5 (electricity) is the same as 3/15.

When you add those together, you can see that 8/15 of the person's income is spent on these two items.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The budget for rent:

(1/3) of 7200 for rent = 7200/3 = 2400 (1)

The budget for electricity:

(1/5) of 7200 for electricity = 7200/5 = 1440 (2)