Question

A group of mountain climbers begin a expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day . Write and solve a linear equation to find the number of days their food will last

Answer 1

The equation representing total food consumption in
`x` days can be given as:

`y=12x`

where
`y` represents total food taken which is =250 pounds and
`x` represnts the number of days the food will last.

The food will last for
`20(5)/(6)` days.

Explanation:

Total pounds of food taken at the beginning = 250 pounds

Food consumed per day = 12 pounds

Let the total food at the beginning be =
`y` pounds

Let number of days the food will last be =
`x` days

Using unitary method to find the food consumed in
`x` days.

If in 1 day food consumed = 12 pounds

Then, in
`x` days food consumption =
`12* x = 12x` pounds

So,the equation representing total food consumption in
`x` days can be given as:

`y=12x`

Total food taken =250 pounds

Plugging in
`y=250` in the equation:

`250=12x`

Solving for
`x`

Dividing both sides by 12.

`(250)/(12)=(12x)/(12)`

`(250)/(12)=x`

Simplifying fractions.

`(125)/(6)=x`

Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.

∴
`x=20(5)/(6)` days.

Thus, the food will last for
`20(5)/(6)` days.