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

Answer:

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 $20\frac{5}{6}$ days.

Step-by-step 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 = $12\times x = 12x$ 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.

$\frac{250}{12}=\frac{12x}{12}$

$\frac{250}{12}=x$

Simplifying fractions.

$\frac{125}{6}=x$

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

∴ $x=20\frac{5}{6}$ days.

Thus, the food will last for $20\frac{5}{6}$ days.