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question:Elyse had x pieces of gum. She gave half to her brother Rick. He gave half of his to his friend Shane. Shane chewed 11 pieces of gum. How many pieces does Shane have left? If we know the answer to the above question is 14, what is the value of unknown variable x?
answer:Elyse had x pieces of gum. She gave half of it to her brother Rick, which means she gave (1/2)*x pieces of gum to Rick. Rick gave half of his to his friend Shane, which means he gave (1/2)*((1/2)*x) = (1/4)*x pieces of gum to Shane. Shane chewed 11 pieces of gum, so he has ((1/4)*x) - 11 pieces of gum left. We are given that Shane has 14 pieces of gum left, so we can write: ((1/4)*x) - 11 = 14. Adding 11 to both sides, we get: (1/4)*x = 25. Multiplying both sides by 4, we get: x = 100. The value of x is 100. 100 The answer is: 100
question:Audrey is 7 years older than Heracles. In 3 years, Audrey will be twice as old as Heracles is now. How old is Heracles now?
answer:Let's assume that Heracles is X years old. If Audrey is 7 years older than Heracles, then Audrey's age is X + 7. In 3 years, Audrey will be X + 7 + 3 = X + 10 years old. If Audrey will be twice as old as Heracles is now in 3 years, then X + 10 = 2X. Subtracting X from both sides of the equation, we get 10 = X. Therefore, Heracles is currently 10 years old. 10 The answer is: 10
question:To be eligible for an algebra class a student must have an average of at least 83% over all four quarters in his or her pre-algebra class. If Fisher had an 82%, 77%, and X in the first three quarters, what is the minimum score he must earn in the 4th quarter to move on to algebra? If we know the answer to the above question is 98, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. Fisher needs to have an average of at least 83% over all four quarters to be eligible for the algebra class. To find the minimum score Fisher must earn in the 4th quarter, we can set up an equation. We know that the average of the four quarters is equal to the sum of the scores divided by 4. The sum of the scores in the first three quarters is 82% + 77% + X. The average of the four quarters must be at least 83%. So, we can write the equation: frac{82% + 77% + X + Y}{4} geq 83% Simplifying the equation, we have: frac{159% + X + Y}{4} geq 83% Multiplying both sides of the inequality by 4 to eliminate the fraction, we get: 159% + X + Y geq 332% Subtracting 159% from both sides of the inequality, we find: X + Y geq 332% - 159% X + Y geq 173% Given that the minimum score Fisher must earn in the 4th quarter is 98, we can substitute it into the equation: 98 + Y geq 173% Subtracting 98 from both sides of the inequality, we find: Y geq 173% - 98 Y geq 75% The value of X is 75. The answer is: 75
question:f Barry has dimes worth 10.00 and his little brother Dan has half that amount but finds 2 more dimes on his way home from school, how many dimes does Dan have?
answer:If Barry has dimes worth 10.00, that means he has 10/0.10 = 100 dimes. If Dan has half the amount of dimes as Barry, that means he has 100/2 = 50 dimes. Since Dan finds 2 more dimes on his way home, he now has 50 + 2 = 52 dimes. Therefore, Dan has 52 dimes. 52 The answer is: 52