Answer :
Answer:
The equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
where [tex]y[/tex] represents total food taken which is =250 pounds and [tex]x[/tex] represnts the number of days the food will last.
The food will last for [tex]20\frac{5}{6}[/tex] 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 = [tex]y[/tex] pounds
Let number of days the food will last be = [tex]x[/tex] days
Using unitary method to find the food consumed in [tex]x[/tex] days.
If in 1 day food consumed = 12 pounds
Then, in [tex]x[/tex] days food consumption = [tex]12\times x = 12x[/tex] pounds
So,the equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
Total food taken =250 pounds
Plugging in [tex]y=250[/tex] in the equation:
[tex]250=12x[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 12.
[tex]\frac{250}{12}=\frac{12x}{12}[/tex]
[tex]\frac{250}{12}=x[/tex]
Simplifying fractions.
[tex]\frac{125}{6}=x[/tex]
Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.
∴ [tex]x=20\frac{5}{6}[/tex] days.
Thus, the food will last for [tex]20\frac{5}{6}[/tex] days.