A stadium has two sections

Tickets for section A cost $a each
Tickets for Section B cost $b each

Johanna paid $105 for 5 section A tickets and 3 section B tickets.
Raiyah Paid $63 for 4 section A tickets and 1 section B ticket

Write 2 equations in a and b to represent the info.
1)5a+3b=105
2)4a+b=63
Is this correct?
And how do i calculate the values of a and b?

The equations are correct.

To solve, I would multiply both sides of the second equation by 3, then subtract equation 2 from 1. The b terms will have subtracted out.

5a +3b =105

- 12a + 3b =189
-7a = -84
; -84 รท -7 =12
a= 12

Yes, you have correctly written the equations to represent the given information:

1) 5a + 3b = 105
2) 4a + b = 63

To calculate the values of a and b, you can use the method of substitution or elimination. I will explain both methods:

1. Substitution Method:
In this method, you isolate one variable in one equation and substitute its value into the other equation.

Let's solve the second equation for b:
From equation 2: 4a + b = 63
Subtract 4a from both sides: b = 63 - 4a

Now, substitute this value of b into the first equation:
5a + 3(63 - 4a) = 105
Distribute 3: 5a + 189 - 12a = 105
Combine like terms: -7a + 189 = 105
Subtract 189 from both sides: -7a = -84
Divide by -7: a = 12

Now, substitute the value of a back into either of the original equations to find b:
Using equation 2: 4(12) + b = 63
48 + b = 63
Subtract 48 from both sides: b = 15

So, the values of a and b are a = 12 and b = 15.

2. Elimination Method:
In this method, you multiply both equations by appropriate constants to make the coefficients of one variable opposite in sign.

Multiply equation 1 by 4 and equation 2 by 5 to make the coefficient of a equal:
4(5a + 3b) = 4(105) -> 20a + 12b = 420
5(4a + b) = 5(63) -> 20a + 5b = 315

Now, subtract the second equation from the first equation to eliminate a:
(20a + 12b) - (20a + 5b) = 420 - 315
Combine like terms: 7b = 105
Divide by 7: b = 15

Substitute this value of b back into either of the original equations to find a:
Using equation 1: 5a + 3(15) = 105
5a + 45 = 105
Subtract 45 from both sides: 5a = 60
Divide by 5: a = 12

So, the values of a and b are a = 12 and b = 15.

Both methods will give you the same values for a and b, so you can use either one to solve the equations.