Respuesta :
[tex]\text{Answer: Number of weeks }=56[/tex]
Explanation:
Since we have given that
[tex]\text{Number of bags of dog food to feed all of the dogs at the animal shelter} =56\frac{37}{40}[/tex][tex]\text{Number of bags of food per week eaten by dogs }= 8\frac{1}{4}[/tex]
So,
[tex]\text{Number of weeks worth of dog food Emma have } =\frac{56\frac{37}{40}}{8\frac{1}{4}}[/tex]
[tex]\text{Number of weeks worth of dog food Emma have }=\frac{2240\times 4}{40\times 4}\\\text{Number of weeks worth of dog food Emma have }=\frac{2240}{40}\\\text{Number of weeks worth of dog food Emma have }=56[/tex]
∴ [tex]\text{Number of weeks worth of dog food Emma have}=56[/tex]
Total bags of dog food to feed the dogs = [tex]56 \frac{37}{40}[/tex] bags
Total bags of food eaten by dogs per week = [tex]8\frac{1}{4}[/tex] bags
We have to determine the number of weeks, worth of dog food which Emma has.
The number of weeks are calculated by dividing the total number of bags of dog food divided by the total bags of food eaten by dogs per week.
So, The number of weeks = [tex]56 \frac{37}{40} \div 8 \frac{1}{4}[/tex]
= [tex]\frac{2277}{40} \div \frac{33}{4}[/tex]
= [tex]\frac{2277}{40} \times \frac{4}{33}[/tex]
= [tex]\frac{2277}{10} \times \frac{1}{33}[/tex]
= [tex]\frac{2277}{330}[/tex]
= [tex]\frac{207}{30}[/tex]
= 6.9
= 7 weeks
So, Emma has dog food for 7 weeks.
