This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems. 1. Step 1: Calculate the amount by which the car's value decreased. The value decreased by (2)/(7) of its original value. Decrease = (2)/(7) × \7700 = 2 × (\7700)/(7) = 2 × \1100 = \2200 Step 2: Calculate the new value of the car. The new value is the original value minus the decrease. New value = \7700 - \2200 = \5500 The correct option is B. The new value of the car is \5500. 2. Step 1: Recall the relationship between LCM, GCF, and two numbers. For two numbers N_1 and N_2, their product is equal to the product of their LCM and GCF: N_1 × N_2 = LCM(N_1, N_2) × GCF(N_1, N_2) Step 2: Substitute the given values into the formula. Given N_1 = 189, LCM = 2079, and GCF = 27. 189 × N_2 = 2079 × 27 Step 3: Solve for the other number, N_2. N_2 = (2079 × 27)/(189) We can simplify by noting that 189 = 7 × 27. N_2 = 2079 × 277 × 27 = (2079)/(7) N_2 = 297 The correct option is E. The other number is 297. 3. Step 1: Evaluate the division inside the first parenthesis. (2)/(3) ÷ (4)/(3) = (2)/(3) × (3)/(4) = (2 × 3)/(3 × 4) = (6)/(12) = (1)/(2) Step 2: Evaluate the multiplication inside the second parenthesis. (4)/(5) × (5)/(6) = (4 × 5)/(5 × 6) = (20)/(30) = (2)/(3) Step 3: Substitute these results back into the original expression. (1)/(2) + (1)/(2) - (2)/(3) Step 4: Perform the addition and subtraction from left to right. ((1)/(2) + (1)/(2)) - (2)/(3) = 1 - (2)/(3) 1 - (2)/(3) = (3)/(3) - (2)/(3) = (1)/(3) The correct option is B. The evaluated expression is (1)/(3). 4. Step 1: Define the original fraction using a variable. Let the numerator of the original fraction be x. The denominator exceeds the numerator by 3, so the denominator is x+3. The original fraction is (x)/(x+3). Step 2: Set up an equation based on the given condition. If 1 is added to the numerator, the new numerator is x+1. The denominator remains unchanged. The new fraction is (x+1)/(x+3). This new fraction is equal to (3)/(4). (x+1)/(x+3) = (3)/(4) Step 3: Solve the equation for x. Cross-multiply: 4(x+1) = 3(x+3) 4x + 4 = 3x + 9 Subtract 3x from both sides: x + 4 = 9 Subtract 4 from both sides: x = 5 Step 4: Find the original fraction. The numerator is x=5. The denominator is x+3 = 5+3 = 8. The original fraction is (5)/(8). The correct option is A (or C, as they are identical). The original fraction is (5)/(8). 3 done, 2 left today. You're making progress.