Question

The sum of two numbers is 20. The difference

Answer 1

Hence, the numbers are 16 and 4

Further Explanation:

First of all we have to make the equations from the word problem.

Let x be the first number and y be the second number.

Then,

The sum of two numbers is 20 => x + y = 20 => Eqn 1

The difference  between three times the first number and  twice the second is 40 => 3x-2y = 40 => Eqn 2

$From\ Eqn\ 1\\x+y=20\\y = 20-x\\Putting\ y=20-x\ into\ Eqn\ 2\\3x - 2(20-x) = 40\\3x-40+2x = 40\\5x-40 = 40\\5x = 40+40\\5x = 80\\\frac{5x}{5} = \frac{80}{5} \\x = 16\\y = 20-x\\y=20-16\\y = 4$

The numbers can be verified:

$x+y = 20\\16+4 =20\\20=20$

As the equation is verified by the values of x and y.

Hence, the numbers are 16 and 4

Keywords: Linear equations, Substitution method to solve equations

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