Linear Application

Question

In a basket are apples for six people.  One-third, one-fourth, one-eighth and one-fifth of the apples in the basket are given to four people, respectively.  The fifth person gets ten apples, leaving one apple for the sixth person.  Find the original number of apples in the basket.

Answer 1

In a basket are apples for six people.  One-third, one-fourth, one-eighth and one-fifth of the apples in the basket are given to four people, respectively.  The fifth person gets ten apples, leaving one apple for the sixth person.  Find the original number of apples in the basket.

Let T represent the number of Total apples in the basket. The following EQUATION relates the math facts from problem.....

1/3T + 1/4T + 1/8T + 1/5T + 10 + 1 = T

Let's add the fractions together using LCD....Least Common Denominator (LCD)

480...just multiply all denominators to find the Least Common Multiple.....(LCM)

160/480T + 120/480T + 60/480T + 96/480T + 10 + 1 = T

add T terms

436/480 T + 11 = T

....solve for T.....

11 = 480/480 T - 436/480 T ....... 11 = 44/480T multiply both sides by 480/44 .....

T = 480/44*11 = 480/4 = 120.......check....

1/3T + 1/4T + 1/8T + 1/5T + 10 + 1 = T ......1/3(120) + 1/4(120) + 1/8(120) + 1/5(120) + 10 + 1 =???

40 + 30 + 15 + 24 + 10 + 1 = 120......That Checks.......