Question

Adam had 30 less balloons than Billy had. After Billy gave 5 balloons to Adam, the number of Adam's balloons was half of the number of Billy's balloons. What was the number of balloons they have together?

Answer 1

Answer:

60 balloons.

Step-by-step explanation:

Let the number of balloons that Adam had be x and number of balloons Billy had be y.  

We have been given that Adam had 30 less balloons than Billy. We can represent this information in an equation as: $x+30=y...(1)$.    

If Billy gave 5 balloons to Adam, Billy will have y-5 balloons and Adam will have x+5 balloons.

We are told that x+5 is half of the y-5. Let us represent this information in an equation.

$2(x+5)=y-5...(2)$

Now we have two equations and to unknowns. Let us solve our system of equations using substitution method.

Upon substituting y's value from equation 1 into equation 2 we will get,

$2(x+5)=x+30-5$

$2(x+5)=x+25$

Upon distributing 2 on left side of our equation we will get,

$2x+10=x+25$

$2x-x+10=25$

$2x-x=25-10$

$x=15$

Therefore, Adam has 15 balloons.

Now let us substitute x=15 in equation 1 to find y.

$15+30=y$

$45=y$

Therefore, Billy has 45 balloons.

Now we will add 45 and 15 to find the number of balloons that Adam and Billy have together.

$\text{Number of balloons Adam and Billy have together}=15+45$

$\text{Number of balloons Adam and Billy have together}=60$

Therefore, Adam and Billy have 60 balloons together.