Brenda thinks of a number y which she squares, then subtracts 5, next multiplies it by 4, subtracts 7, divides it by 3 and finally adds 6. Her answer is 9. What is the value of y?*
Question
Brenda thinks of a number y which she squares, then subtracts 5, next multiplies it by 4, subtracts 7, divides it by 3 and finally adds 6. Her answer is 9. What is the value of y?*
Solution
Let's solve this step by step:
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First, let's write down the equation according to the problem. If we denote the number Brenda thinks of as y, the equation is:
((y^2 - 5) * 4 - 7) / 3 + 6 = 9
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Now, let's simplify the equation. Subtract 6 from both sides:
((y^2 - 5) * 4 - 7) / 3 = 3
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Multiply both sides by 3:
(y^2 - 5) * 4 - 7 = 9
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Add 7 to both sides:
(y^2 - 5) * 4 = 16
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Divide both sides by 4:
y^2 - 5 = 4
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Add 5 to both sides:
y^2 = 9
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Finally, take the square root of both sides. Remember that the square root of a number can be either positive or negative:
y = ±3
So, the number Brenda thought of could be either 3 or -3.
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