Question

three friends are buying a gift for a friend. declan contributes 4 dollars more than \dfrac{1}{4} ​4 ​ ​1 ​​ the cost of the gift, ed contributes 1 dollar less than \dfrac{1}{3} ​3 ​ ​1 ​​ the cost of the gift, and frank contributes the remaining 22 dollars. what is the cost of the gift?

Answer 1

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Answer 2

Answer:

The cost of the gift is $ 60.

Step-by-step explanation:

Let the cost of the gift is x dollars,

Since, Declan contributes 4 dollars more than $\frac{1}{4}$ of the cost of the gift,

So, Declan's contribution = $\frac{x}{4}+4$

Also, Ed contributes 1 dollar less than $\frac{1}{3}$ of the cost of the gift,

So, Ed's contribution = $\frac{x}{3}-1$

Again frank contributes the remaining 22 dollars,

∵ Only three person contributed,

Thus, the total price of the cost = $\frac{x}{4}+4+\frac{x}{3}-1+22$

$=\frac{3x+4x}{12}+25$

$=\frac{7x}{12}+25$

$\implies \frac{7x}{12}+25 = x$

$\frac{7x}{12}=x-25$

$7x = 12x - 300$

$300 = 12x - 7x$

$300=5x \implies x = \frac{300}{5}=60$

Hence, the cost of the gift is $ 60.