Liz spent 1/2, 1/3, 1/4, $15 left. Birthday money?
- A. $360
- B. $180
- C. $120
- D. $60
Correct Answer & Rationale
Correct Answer: D
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
Other Related Questions
Which would be read as 'two million three hundred six thousand nine hundred thirty-four'?
- A. 2,036,934
- B. 2,306,934
- C. 2,360,934
- D. 2,369.03
Correct Answer & Rationale
Correct Answer: B
Option B, 2,306,934, accurately represents 'two million three hundred six thousand nine hundred thirty-four.' The number is broken down as follows: 2 million (2,000,000), 300 thousand (300,000), 6 thousand (6,000), 900 (900), and 30 (30), culminating in 2,306,934. Option A, 2,036,934, incorrectly includes only 30 thousand instead of 300 thousand. Option C, 2,360,934, misplaces the hundreds, showing 360 thousand instead of 306 thousand. Option D, 2,369.03, is not a whole number representation and introduces decimal values, which are irrelevant in this context.
Option B, 2,306,934, accurately represents 'two million three hundred six thousand nine hundred thirty-four.' The number is broken down as follows: 2 million (2,000,000), 300 thousand (300,000), 6 thousand (6,000), 900 (900), and 30 (30), culminating in 2,306,934. Option A, 2,036,934, incorrectly includes only 30 thousand instead of 300 thousand. Option C, 2,360,934, misplaces the hundreds, showing 360 thousand instead of 306 thousand. Option D, 2,369.03, is not a whole number representation and introduces decimal values, which are irrelevant in this context.
Joe’s age 4 more than 3x Amy’s. Equation?
- A. A=J/3+4
- B. A=3J+4
- C. J=3A+4
- D. J=3(A+4)
Correct Answer & Rationale
Correct Answer: C
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
Greatest?
- A. 245 thousandths
- B. 24 hundredths
- C. 3 tenths
- D. 2 fifths
Correct Answer & Rationale
Correct Answer: D
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
Rounds to 87.5 in tenths?
- A. 88
- B. 87.56
- C. 87.459
- D. 87.05
Correct Answer & Rationale
Correct Answer: C
When rounding to the nearest tenth, the digit in the hundredths place determines whether to round up or down. For 87.5, the first digit after the decimal is 5, indicating that we round up. Option A (88) rounds to the nearest whole number, not the nearest tenth. Option B (87.56) rounds to 87.6, which is higher than 87.5. Option D (87.05) rounds to 87.1, which is lower. Only option C (87.459) rounds to 87.5 when considering the tenths place, making it the only valid choice for rounding to 87.5 in tenths.
When rounding to the nearest tenth, the digit in the hundredths place determines whether to round up or down. For 87.5, the first digit after the decimal is 5, indicating that we round up. Option A (88) rounds to the nearest whole number, not the nearest tenth. Option B (87.56) rounds to 87.6, which is higher than 87.5. Option D (87.05) rounds to 87.1, which is lower. Only option C (87.459) rounds to 87.5 when considering the tenths place, making it the only valid choice for rounding to 87.5 in tenths.