Question

A man is 5 years older than his wife and their product is 750 find the age of husband and wife​

Answer 1

Answer

• Age of wife = 25 years.
• Age of husband = 30 years.

To Find

• The age of husband and wife.

Given

• A man is 5 years older than his wife.
• The product of their ages = 750.

Step By Step Explanation

Assumption :

Let us assume the age of wife be x and the age of husband be x + 5.

Equation :

According to the question equation will be ⤵

$\bigstar \: \: \underline {\boxed{\bold{ \red{(x)(x + 5) = 750}}}}$

Solution of the equation :

Let us solve the above equation to find the value of x.

$\longmapsto \sf(x)(x + 5) = 750 \\ \\ \longmapsto \sf {x}^{2} + 5x = 750 \\ \\\longmapsto \sf {x}^{2} + 5x - 750 = 0 \\ \\ \bold{ By \: splitting \: the \: middle \: term \downarrow} \\ \\ \longmapsto \sf {x}^{2} + 30x - 25x - 750 = 0 \\ \\\longmapsto \sf x(x + 30) - 25(x + 30) \\ \\\longmapsto \sf (x + 30)(x - 25) = 0 \\ \\\longmapsto \tt \red{x + 30 = 0 \implies \: x = - 30} \\ \\ \longmapsto \bold{ \green{x - 25 = 0 \implies \: x = 25}}\:\: \bigstar$

Age is never negative.

Therefore, the age of wife = 25 years and the age of husband = x + 5 => 30 years.

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