Question

The product of two integers is 112. One number is four more than three times the other. Which of the following equations could be used to find one of the numbers?

Answer 1

Answer:

The  equations could be used to find one of the numbers is, $3a^2 + 4a =112$

Step-by-step explanation

Let two integers be a and b.

As per the given statement:

The product of two integers is 112.

⇒  $ab =112$          ......[1]

Also, One number is 4 more than three times the other.

⇒b = 3a +4                      ......[2]

Now substitute equation [1] in [2] we get

$a(3a+4) =112$

Using distributive property i.e, $a \cdot (b+c) = a\cdot b + a\cdot c$

$(a)(3a)+ 4a = 112$

Simplify:

$3a^2 + 4a =112$

therefore, the equation that could be used to find one of the numbers is;

$3a^2 + 4a =112$