It cost $35 for one adult and two children to attend a show.it cost $60 for two adults and three children to attend the same show.How much dose it cost one adult to attend the show?
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Answer:
$15
Step-by-step explanation:
This question can be solved with the use of a system of equations.
Start by defining the variables that will be used:
Let the cost of 1 adult and 1 child to attend the show be $a and $c respectively.
Form 2 equations and label them:
a +2c= 35 -----(1)
2a +3c= 60 -----(2)
Let's solve by elimination. Since the question is only asking for the cost for an adult to attend the show, we can work to eliminate the c term. This can be done by ensuring that the coefficients of c in both equation has the same numerical value (the sign does not really matter for now). In this case, we can make the coefficient of c to be 6 since it is the lowest common multiple of 2 and 3.
(1) ×3: 3a +6c= 105 -----(3)
(2) ×2: 4a +6c= 120 -----(4)
Since the coefficient of c in both (3) and (4) are +6, we can subtract one equation from the other to eliminate the term c.
(4) -(3):
(4a +6c) -(3a +6c)= 120 -105
Expand:
4a +6c -3a -6c= 15
a= 15
Thus, it costs $15 for one adult to attend the show.
Additional:
Do check out the following for an example on solving a system of equations by the substitution method!
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Answer:
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Step-by-step explanation:
Enter the correct value of x.
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Answer:
30
Step-by-step explanation:
Adjacent angles of a parallelogram add up to 180 degrees, meaning that (3x)+(x+60)=180 degrees. You can use this to set up the following equation:
3x+x+60=180
4x=120
x=30 degrees. Hope this helps!
Final answer:
In a parallelogram, opposite angles are equal. Therefore, set 3x (angle A) equal to x + 60 (angle D). Solving for x, we get x = 30.
Explanation:
In this case, we're working with a parallelogram, and one of the properties of a parallelogram is that its opposite angles are equal. That means that ∠A is equal to ∠D. So we set (3x) equal to (x + 60).
To determine the value of x, we can solve this equation:
3x = x + 60. Subtract x from both sides to get 2x = 60, then divide by 2 to get x = 30.
So, the value of x that makes ABCD a parallelogram is 30.
Learn more about Parallelogram here:
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Hope this helps!
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