Angelo shot 4 darts at a target. Three landed in area A and one landed in area B giving him a total score of 16. Dan shot 4 darts too. One landed in A and three landed in B giving a total of 24. What score would be made hitting B three times?
To find the score made by hitting B three times, we need to determine the individual score values for hitting areas A and B. Let's assign variables:
Let's designate the score for hitting area A as "a" and the score for hitting area B as "b".
From the given information, we know that Angelo shot 4 darts and landed 3 in area A and 1 in area B, resulting in a total score of 16. This gives us the equation: 3a + b = 16.
Similarly, Dan shot 4 darts with 1 dart landing in area A and 3 darts landing in area B, resulting in a total score of 24. This gives us the equation: a + 3b = 24.
Now, we can solve this system of equations to find the values of "a" and "b", and subsequently calculate the score if B is hit three times.
Multiplying the first equation by 3, we get: 9a + 3b = 48.
Subtracting the second equation from this multiplied form, we have:
(9a + 3b) - (a + 3b) = 48 - 24.
8a = 24.
Dividing both sides by 8, we find: a = 3.
Substituting the value of "a" into either of the original equations, we find: 3 + 3b = 24.
Subtracting 3 from both sides gives us: 3b = 21.
Dividing both sides by 3, we find: b = 7.
So, the score for hitting area B is 7.
To calculate the score of hitting B three times, we multiply the score value of hitting B by 3:
Score = 7 * 3 = 21.
Therefore, hitting area B three times would result in a score of 21.