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 By: t.h.seah (offline)  Thursday, July 27 2017 @ 07:58 PM CDT (Read 1149 times)
t.h.seah

pls help .

Valerie, Jake and Zechariah shared the cost of a present. 3/5 of Zechariah's share was equal to 1/3 the total of Jake's and Valerie's share. 2/3 of Jake's share was equal to 1/3 of the total of Zechariah's and Valerie's share. Valerie paid \$30 less then Zechariah. How much did the present cost?

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Registered: 07/28/11
Posts: 3

 By: echeewh (offline)  Saturday, July 29 2017 @ 11:30 PM CDT
echeewh

Hey <t.h.seah>,

Following is my worked solution :

(3/5)Z = (1/3) (J + V)

Given that both fractions make up equal value or amounts, we make the numerator of both fractions the same giving its equivalent fractions. This is applying the <Equal Concept> method, and we have ...

(3/5)Z = (3/9) (J + V)

At first, Z = 5u; (J + V) = 9u; Total = 14u --- (1)

(2/3)J = (1/3) (Z + V)

Using <Equal Concept> method, we have ...

(2/3)J = (2/6) (Z + V)

At first, J = 3u; (Z + V) = 6u; Total = 9u --- (2)

As the cost of the present is the same in both cases, the total in (1) and (2) should be the same.

Hence, the common multiple of 14 and 9 is 126.

(1)x9:
Z = 45u; (J + V) = 81u; Total = 126u --- (3)

(2)x14:
J = 42u; (Z + V) = 84u; Total = 126u --- (4)

Hence, Z = 45u; J = 42u; V = 126u - 45u - 42u = 39u

Given that Valerie paid \$30 less then Zechariah, we have ...

Z - V = 30
45u - 39u --> 30
6u --> 30
1u --> 30 ÷ 6 = 5

Therefore the cost of the present = 126u --> 126 × 5 = \$630

======

Trust this helps.

Do let me know again if this is different from the <Anskey> or if there is further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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