Respuesta :
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: [tex]x+30=y...(1)[/tex].
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.
[tex]2(x+5)=y-5...(2)[/tex]
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,
[tex]2(x+5)=x+30-5[/tex]
[tex]2(x+5)=x+25[/tex]
Upon distributing 2 on left side of our equation we will get,
[tex]2x+10=x+25[/tex]
[tex]2x-x+10=25[/tex]
[tex]2x-x=25-10[/tex]
[tex]x=15[/tex]
Therefore, Adam has 15 balloons.
Now let us substitute x=15 in equation 1 to find y.
[tex]15+30=y[/tex]
[tex]45=y[/tex]
Therefore, Billy has 45 balloons.
Now we will add 45 and 15 to find the number of balloons that Adam and Billy have together.
[tex]\text{Number of balloons Adam and Billy have together}=15+45[/tex]
[tex]\text{Number of balloons Adam and Billy have together}=60[/tex]
Therefore, Adam and Billy have 60 balloons together.
