Question

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gives 7 peaches to a 5th person. If there are 4 peaches remaining, what was the original number of peaches in the basket?

Answer 1

Answer:

$\frac{1429}{120}$ or $11\frac{109}{120}$

Step-by-step explanation:

Given:

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gives 7 peaches to a 5th person.

Remaining peaches = 4

We need to find the original number of peaches in the basket.

The farmer gives the total number of peaches = $\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7$

Let x be the former gives the total number of peaches

We multiply and divide by 120 in right side of the above equation because of 120 is divided by all given denominator and then simplify.

$x = \frac{120}{120}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7)$

$x = \frac{1}{120}(\frac{120}{3}+\frac{120}{4}+\frac{120}{5}+\frac{120}{8}+7\times 120)$

$x = \frac{1}{120}(40+30+24+15+840)$

$x = \frac{1}{120}(949)$

$x = \frac{949}{120}$

We add the remaining peaches by given peaches for the original number of peaches in the basket.

Original number of peaches = $\frac{949}{120}+4$

Original number of peaches = $\frac{949+4\times 120}{120}$

Original number of peaches = $\frac{949+480}{120}$

Original number of peaches = $\frac{1429}{120}$

Original number of peaches = $11\frac{109}{120}$

Therefore the original number of peaches in the basket is $\frac{1429}{120}$ or $11\frac{109}{120}$