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.
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Here are the solutions to the word problems: 4. Step 1: Define the variables. Let w be the number of lavender soap bars sold. Number of lemongrass soap bars sold = w - 6. Step 2: Formulate the equation using the given information that 49 bars of lemongrass soap were sold. w - 6 = 49 Step 3: Solve for w. w = 49 + 6 w = 55 The shopkeeper sold 55 bars of lavender soap. 5. Step 1: Define the variables. Amount of apple juice = 2(1)/(4) litres. Amount of orange juice = d litres. Total fruit punch = 5 litres. Step 2: Formulate the equation. 2(1)/(4) + d = 5 Step 3: Convert the mixed number to an improper fraction. 2(1)/(4) = (2 × 4 + 1)/(4) = (9)/(4) Step 4: Substitute the fraction into the equation. (9)/(4) + d = 5 Step 5: Solve for d. d = 5 - (9)/(4) d = (5 × 4)/(4) - (9)/(4) d = (20)/(4) - (9)/(4) d = (11)/(4) Step 6: Convert the improper fraction back to a mixed number. d = 2(3)/(4) Mr Henderson made 2(3)/(4) litres of orange juice. 6. Step 1: Define the variables. Let p be the number of pencils Nick has. Number of pens Nick has = p + 3. Total number of pencils and pens = 11. Step 2: Formulate the equation. p + (p + 3) = 11 Step 3: Simplify the equation. 2p + 3 = 11 Step 4: Solve for p. 2p = 11 - 3 2p = 8 p = (8)/(2) p = 4 Nick has 4 pencils. Last free one today — make it count tomorrow, or type /upgrade for unlimited.