Question

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation?

Answer 1

y=2(x+3) and y=(3x)+5 best represent this situation

Answer 2

The following system represents the situation :

`\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.`

And the solution is
`(x,y)=(1,8)`

Explanation:

In order to write the equations that represent the situation we need to read carefully the question.

The first sentence is : '' A number, y, is equal to twice the sum of a smaller number and 3.''

We define the following variables :

y : '' The largest number ''

x : '' The smallest number ''

From the first sentence we can write the first equation of the system :

`y=2(x+3)` (I)

The second sentence is : '' The larger number is also equal to 5 more than 3 times the smaller number. ''

From this sentence we can write :

`y=5+3x` (II)

Now we can make our system we equations (I) and (II) :

`\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.`

If we want to solve the system, we can use the equation (II) in the equation (I) :

`5+3x=2(x+3)`

`5+3x=2x+6`

`x=1` ⇒ Using x = 1 in (I) or (II) ⇒

`y=2(x+3)`

`y=2(1+3)`

`y=2.(4)`

`y=8`