Steps to solve 3 (x -5) + 7 x = 65
2 answers:
To solve this, you need to isolate/get the variable "x" by itself in the equation:
3(x - 5) + 7x = 65 Distribute 3 into (x - 5)
(3)x + (3)(-5) + 7x = 65
3x - 15 + 7x = 65 Combine like terms(terms that have the same variable and power/exponent), or combine 3x and 7x
10x - 15 = 65 Add 15 on both sides
10x - 15 + 15 = 65 + 15
10x = 80 Divide 10 on both sides to get "x" by itself
x = 8
PROOF
3(x - 5) + 7x = 65 Substitute/plug in 8 into "x" since x = 8
3(8 - 5) + 7(8) = 65
3(3) + 56 = 65
9 + 56 = 65
65 = 65
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Answer: 15/91 which is choice B
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There are two methods to find this answer.
Method 1) We have 6 girls and 8+6 = 14 students. The probability of picking a girl is 6/14 = 3/7. After the first girl is chosen, we have 5 girls left out of 14-1 = 13 students overall. The probability of picking another girl (assuming the first selection was a girl) is 5/13. Multiply these probabilities: (3/7)*(5/13) = (3*5)/(7*13) = 15/91
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Method 2) We can use the nCr combination formula. Order does not matter.
We have nCr = 6 C 2 = 15 ways to pick 2 girls. See the attached image below for the steps (figure 1)
Out of nCr = 14 C 2 = 91 ways to pick 2 students. See the attached image below for the steps (figure 2)
So that's another way to get the answer 15/91.
