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A baker is using a cookie recipe that calls for 2 ? cups of flour to yield 36 cookies. How much flour will the baker need to make 90 cookies using the same recipe?
- A. 5 ? cups
- B. 6 ? cups
- C. 4 ? cups
- D. 10 ? cups
Correct Answer: B
Rationale: To find the amount of flour needed for 90 cookies, first calculate the flour per cookie: (2 ? cups / 36 cookies) = (8/36) = (2/9) cups per cookie. Then multiply by 90: (2/9) × 90 = 20 cups.
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What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.
A consumer makes a $400 down payment on a television that costs $1,570. How many months will it take to pay off the television with monthly payments of $100? (Assume no interest)
- A. 16
- B. 12
- C. 11
- D. 15
Correct Answer: B
Rationale: To determine the number of months needed to pay off the television, subtract the down payment from the total cost: $1,570 - $400 = $1,170. Next, divide the remaining amount ($1,170) by the monthly payment of $100 to find the number of months: $1,170 · $100 = 11.7 months. Since you cannot make a fraction of a monthly payment, the consumer will need to make 12 monthly payments to fully pay off the television.
A recipe calls for 2 1/2 cups of flour to yield 36 cookies. How much flour will be needed to make 90 cookies using the same recipe?
- A. 6 1/2 cups
- B. 10 1/2 cups
- C. 5 1/2 cups
- D. 4 1/2 cups
Correct Answer: A
Rationale: To determine the amount of flour needed for 90 cookies using the same recipe, set up a proportion: (90 cookies / 36 cookies) * 2.5 cups = 6.25 cups, which simplifies to 6 1/2 cups of flour. Therefore, to make 90 cookies, you will need 6 1/2 cups of flour, based on the original recipe's ratio of flour to cookies.
A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that saves an additional 25% off of the sale price. If the consumer pays $237 for the recliner, what is the original price of the recliner to the nearest dollar?
- A. $451
- B. $527
- C. $316
- D. $431
Correct Answer: A
Rationale: To find the original price, start by letting x represent the original price. The sale price is 30% less than x, which means it is 70% of x (100% - 30% = 70%). After the additional 25% off coupon, the consumer pays 75% of the sale price (100% - 25% = 75%). Setting up the equation: 0.75 * 0.7 * x = $237. Solving for x gives x = $451, which is the original price of the recliner.
A gumball machine contains red, orange, yellow, green, and blue gumballs. Twenty percent of the gumballs are red, 30% are orange, 5% are yellow, 10% are green, and the rest are blue. If there are a total of 120 gumballs, how many more blue gumballs are there than yellow gumballs?
- A. 48
- B. 36
- C. 30
- D. 42
Correct Answer: B
Rationale: First, calculate the number of gumballs of each color: Red = 0.20 x 120 = 24 gumballs, Orange = 0.30 x 120 = 36 gumballs, Yellow = 0.05 x 120 = 6 gumballs, Green = 0.10 x 120 = 12 gumballs. The total number of gumballs of the mentioned colors is 24 + 36 + 6 + 12 = 78 gumballs. Therefore, the number of blue gumballs is 120 - 78 = 42 gumballs. To find the difference between the number of blue and yellow gumballs, subtract the number of yellow gumballs from the number of blue gumballs: 42 - 6 = 36. Therefore, there are 36 more blue gumballs than yellow gumballs.