Question

One number is five times another number. Their sum is 42. What are the two numbers?

Answer 1

Answer:

7 and 35

Step-by-step explanation:

Let one number be x and the other number be y

"one number is five times another number"

Expressed mathematically: y = 5x --- -eq 1

"their sum is 42"

Expressed mathematically : x + y = 42 ------ eq2

Now we have a system of equations with 2 equations and 2 unknowns, we can solve this easily by substitution

From equation 2,

x + y = 42   (substitute eq 1 into eq 2)

x + (5x) = 42

6x = 42   (divide both sides by 6)

x = 42/6 = 7 (answer)

substituting this back into equation 1:

y = 5x

y = 5(7)

y = 35 (answer)

Answer 2

After solving the above word sentence, the two numbers are 35 and 7 respectively.

• Let the first number be a.

• Let the second number be b.

In this exercise, you're required to find two numbers by translating the word sentence into an algebraic expression and then solving for the unknown variables (a and b).

Translating the word sentence into an algebraic expression, we have;

One number is five times another number:

$a = 5b$  .....equation 1

Their sum is 42:

$a + b = 42$   ...equation 2

Substituting eqn 1 into eqn2, we have:

$5b + b = 42\\\\6b = 42\\\\b = \frac{42}{6}$

b = 7

To find the first number:

$a = 5b$

$a = 5(7)$

a = 35

Therefore, the two numbers are 35 and 7 respectively.

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