Question

Brent spends $450 on his monthly bills. Of this amount, 15% is for utilities, 1/5 is for internet services, and 1/7 Is for phone services.

If the rest of the total amount is for food, how much money does brent have for food

Answer 1

$213

Explanation:

We can solve for the amount of money Brent has for food after paying his monthly bills with the equation:

`x=\$420(100\% - u - i - p)`

where:

• 
  `u = \text{amount spent on utilities}`
• 
  `i = \text{amount spent on internet}`
• 
  `p = \text{amount spent on phone}`

↓ plugging in the given amounts

`x = \$420\!\left(100\% - 15\% - (1)/(5)-(1)/(7)\right)`

↓ converting all values to fractions

`x = \$420\!\left(1 - (3)/(20) - (1)/(5)-(1)/(7)\right)`

↓ converting all fractions to a common denominator

`x = \$420\!\left((140)/(140) - (21)/(140) - (28)/(140)-(20)/(140)\right)`

↓ rewriting all as one fraction

`x = \$420\!\left((140 - 21 - 28 - 20)/(140)\right)`

↓ simplifying the numerator

`x = \left((\$420\cdot 71)/(140)\right)`

↓ canceling a factor of 140 in the numerator and denominator

`x = \left((\$3\,\cdot\, \\ot\!\!\!140\cdot 71)/(\\ot\!\!\!140)\right)`

`x = \$3 \cdot 71`

↓ evaluating the multiplication

`\boxed{x=\$213}`

So, Brent has $213 left to spend on food after paying his monthly bills.