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**

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Trust this helps.

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

Cheers,

Edward