Question

The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the

Answer 1

Answer:

15

Step-by-step explanation:

The key to most problems of this type is carefully translating the word problem into math ... an equation.

"The sum of two numbers is 48."

"Sum": Add

"two numbers": we'll need two numbers... let's call them x & y

"is": =

"48": 48

So, the first sentence means:  $x+y=48$

Note that we have two unknowns here.  To solve for them, we'll need another equation... at least as many equations as unknowns (2 unknowns, needs 2 equations).

"If one number is three more than twice the second number..."

"one number": x

"is": =

"three more than": +3

"twice": 2*

"the second number": y

So, the second sentence introductory clause means: $x=2y+3$

Systems of equations

We have a system of equations. We need as many equations as we have unknowns.  We currently have two equations, and two unknowns.  Let's try to solve the system:

$x+y=48$

$x=2y+3$

There are two main methods to solve systems of equations:  Substitution & Elimination

To use the Substitution Method, we'll need to isolate one of the variables in one of the equations, substitute, and solve.

To use the Elimination Method, we'll need to align like terms, find or build matching coefficients with opposite signs, add to eliminate, and solve.

Given that equation 2 already has x isolated, this system is already ready to use the Substitution method, so let's do that.

Solving a system with the Substitution Method

$x+y=48\\x=2y+3$

$(2y+3) + y = 48$

$2y+3 + y = 48$

$3y+3 = 48$

$3y= 45$

$y= 15$

To find x, substitute back into one of the equations:  Equation 2 already has x isolated, so it will be easy to solve for x.

$x=2(15)+3$

$x=30+3$

$x=33$

So the solution we found is x=33 and y=15.

Check to make sure it satisfies the original conditions:

The sum of the numbers is 48:

$x+y=(33)+(15)\\x+y=48$

One number is three more than twice the second number

$x=2y+3$

$(33)\text{ ?=? }2(15)+3$

$33=33$

Our answer satisfies all of the original conditions, so our answer works.

Answering the question

The question finally asks, "...which of the following is the smaller number?"

Of the two numbers, the smaller number is 15.

Answer 2

Answer:

15

Step-by-step explanation:

"one number is three more than twice the second number"

15 * 2 = 30

30 + 3 = 33

15 + 33 = 48