A stadium have to section a & B .
tickets for section A cost $A each .
tickets for section B cost $B each .
johanna paid $105 for 5 section A and 3 section B.
raiyah paid $63 for 4 section A and 1 section B .
i) Write two eguations
ii) Calculate the value of A and B
so baisically multiply the 2nd equation by 3 so you can subtract the 3bs let me show you
105=5a+3b
-189=12a+3b
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-84=-7a
12=a
then substitute
105=5(12)+3B
105=60+3B
45=3B
15=B
:)
i) 105 = 5A + 3B
63 = 4A + 1B
ii)you solve this system equation by either by substitution or elimination
cheers
i) Let's set up the equations using the given information.
Let A represent the cost of a ticket for section A.
Let B represent the cost of a ticket for section B.
From the first sentence, we know that there are two sections: A and B.
From the second sentence, we know that Johanna bought 5 tickets for section A and 3 tickets for section B, paying a total of $105.
From the third sentence, we know that Raiyah bought 4 tickets for section A and 1 ticket for section B, paying a total of $63.
Equation 1: 5A + 3B = 105
Equation 2: 4A + B = 63
ii) To calculate the values of A and B, we can solve this system of equations.
Using the elimination method, multiply Equation 2 by 3 to eliminate B:
3(4A + B) = 3(63)
12A + 3B = 189
Now, we can subtract Equation 1 from the modified Equation 2:
(12A + 3B) - (5A + 3B) = 189 - 105
12A - 5A + 3B - 3B = 84
7A = 84
Divide both sides of the equation by 7:
7A/7 = 84/7
A = 12
Now that we have the value of A, we can substitute it back into Equation 1 to find B:
5(12) + 3B = 105
60 + 3B = 105
3B = 105 - 60
3B = 45
Divide both sides of the equation by 3:
3B/3 = 45/3
B = 15
Therefore, the value of A is $12 and the value of B is $15.
i) To write two equations based on the given information, we can identify the total cost paid by each person for the tickets they purchased.
Let's assign the variables:
A = the cost of a ticket in section A
B = the cost of a ticket in section B
The total cost paid by Johanna can be found by multiplying the number of tickets in each section with their respective costs:
Total cost paid by Johanna = (5 * A) + (3 * B)
Similarly, the total cost paid by Raiyah can be found using the same logic:
Total cost paid by Raiyah = (4 * A) + (1 * B)
ii) To calculate the values of A and B, we need to solve the two equations from part (i) simultaneously. Using the given information:
Johanna paid $105 for 5 section A and 3 section B. Hence, we can write:
(5 * A) + (3 * B) = 105
Raiyah paid $63 for 4 section A and 1 section B. Hence, we can write:
(4 * A) + (1 * B) = 63
We can now solve these equations to find the values of A and B.