Question

Thomas and Randy had some blue and yellow handkerchiefs. 1/4 of Thomas' handkerchief and 3/7 of Randy's handkerchiefs are blue. Thomas and Randy have the same amount of yellow handkerchiefs. If the difference between the number of handkerchiefs they have is 10, how many handkerchiefs do they have in total?

Answer 1

74 handkerchief

Explanation:

Let the number of Thomas' and Randy's handkerchief be T and R respectively.

Thomas

blue ----- ¼T

yellow ----- 1T -¼T= ¾T

Randy

blue -----
`(3)/(7)`R

yellow -----
`(4)/(7)`R

Since they have the same number of yellow handkerchiefs,

¾T= 4/7 R

Multiply by 28 on both sides,

(since 28 is the lowest common multiple of 4 and 7)

21T= 16R -----(1)

From this we can see that R is greater than T.

Hence, given that the difference between R and T is 10,

R= T +10 -----(2)

Subst. (2) into (1):

21T= 16 (T +10)

21T= 16T +160 (expand)

21T -16T= 160

5T= 160 (simplify)

T= 160 ÷5 (÷5 on both sides)

T= 32

Subst. into (2):

R= 32 +10

R= 42

Thus, total number of handkerchief

= 32 +42

= 74