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?

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: .    

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.

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,

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

Therefore, Adam has 15 balloons.

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

Therefore, Adam and Billy have 60 balloons together.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

c

-by-step explanation:

it would be c