Write these word problems in mathematical language (without working out the answers): a) the difference between 69 and 43 b) the sum of 112 and 28 c) one third of 24 increased by 8 d) the square root of 16 is equal to the square of 2 e) 15 less than 99 f) 20 more than 16.

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Asked on July 28, 2026Mathematics

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.

Accepted Answer · 2026-07-28T16:20:08.866Z

1. Write these word problems in mathematical language (without working out the answers): a) The difference between 69 and 43: 69 - 43 b) The sum of 112 and 28: 112 + 28 c) One third of 24 increased by 8: (1)/(3) × 24 + 8 d) The square root of 16 is equal to the square of 2: sqrt(16) = 2^2 e) 15 less than 99: 99 - 15 f) 20 more than 16: 16 + 20 2. Find the values of the letters in the following flow diagrams: a) Step 1: Calculate a, b, c by multiplying the input by 3. a = 2 × 3 = 6 b = 8 × 3 = 24 c = 16 × 3 = 48 Step 2: Calculate d, e, f by adding 6 to a, b, c. d = a + 6 = 6 + 6 = 12 e = b + 6 = 24 + 6 = 30 f = c + 6 = 48 + 6 = 54 The values are: a=6, b=24, c=48, d=12, e=30, f=54 c) Step 1: Determine the value of g using any input-output pair. Using the first pair: 1 + g = 22 g = 22 - 1 g = 21 Step 2: Verify g with other pairs (optional, but good for checking). 16 + 21 = 37 49 + 21 = 70 The value is: g=21 3. Write these phrases as expressions (write the unknown number as x): a) A number is decreased by the square of 4: x - 4^2 b) The product of 6 and a number is increased by 10: 6x + 10 c) A number divided by 3 is added to the square of that number: (x)/(3) + x^2 d) A number multiplied by 5 is subtracted from 25: 25 - 5x e) Half of a number is added to one third of that number: (x)/(2) + (x)/(3) f) 2 less than the product of a number and 8: 8x - 2 4. Think of a number. Add 5. Multiply the sum by 2. Subtract 1. Write an expression using x for the unknown. Find the value of this expression if x = 12.5. Step 1: Write the expression. Let the unknown number be x. Add 5: x + 5 Multiply the sum by 2: 2(x + 5) Subtract 1: 2(x + 5) - 1 The expression is: 2(x + 5) - 1 Step 2: Find the value of the expression when x = 12.5. 2(12.5 + 5) - 1 2(17.5) - 1 35 - 1 34 The value of the expression is: 34 5. Copy and complete the following table: Step 1: Calculate the output for the given input values. For x = -1: 3(-1) - 4 = -3 - 4 = -7 For x = 0: 3(0) - 4 = 0 - 4 = -4 For x = 3: 3(3) - 4 = 9 - 4 = 5 For x = 10: 3(10) - 4 = 30 - 4 = 26 Step 2: Find the input x when the output is 250. 3x - 4 = 250 3x = 250 + 4 3x = 254 x = (254)/(3) x = 84.67 (approximately) The completed table is: |c|c|c|c|c|c| Input (x) & -1 & 0 & 3 & 10 & (254)/(3) \\ Output (3x - 4) & -7 & -4 & 5 & 26 & 250 \\ 6. If a = 2, b = 6 and c = 5, find the values of these expressions: a) 3b - a 3(6) - 2 = 18 - 2 = 16 The value is: 16 b) 3(b - a) 3(6 - 2) = 3(4) = 12 The value is: 12 c) a + b - c 2 + 6 - 5 = 8 - 5 = 3 The value is: 3 d) 4b - 2c 4(6) - 2(5) = 24 - 10 = 14 The value is: 14 7. Write an expression to describe the relationship of the data in the tables: a) Observe the relationship between m and n: 7 - 5 = 2 10 - 8 = 2 14 - 12 = 2 19 - 17 = 2 The output n is always 2 more than the input m. The expression is: n = m + 2 b) Observe the relationship between x and y: For x = -1, y = -2 y = 2x For x = -4, y = -8 y = 2x For x = -8, y = -16 y = 2x For x = -16, y = -40 y = 2.5x The relationship y = 2x holds for the first three pairs. Assuming there might be a typo in the last value of y (it should be -32 for y=2x to hold), the most consistent expression for the majority of the data is: y = 2x 8. What number doubled and added to 12 gives 20? Step 1: Set up the equation. Let the number be x. 2x + 12 = 20 Step 2: Solve for x. 2x = 20 - 12 2x = 8 x = (8)/(2) x = 4 The number is: 4 Send me the next one 📸

Accepted Answer · 2026-07-28T16:20:08.866Z

1. Write these word problems in mathematical language (without working out the answers): a) The difference between 69 and 43: 69 - 43 b) The sum of 112 and 28: 112 + 28 c) One third of 24 increased by 8: (1)/(3) × 24 + 8 d) The square root of 16 is equal to the square of 2: sqrt(16) = 2^2 e) 15 less than 99: 99 - 15 f) 20 more than 16: 16 + 20 2. Find the values of the letters in the following flow diagrams: a) Step 1: Calculate a, b, c by multiplying the input by 3. a = 2 × 3 = 6 b = 8 × 3 = 24 c = 16 × 3 = 48 Step 2: Calculate d, e, f by adding 6 to a, b, c. d = a + 6 = 6 + 6 = 12 e = b + 6 = 24 + 6 = 30 f = c + 6 = 48 + 6 = 54 The values are: a=6, b=24, c=48, d=12, e=30, f=54 c) Step 1: Determine the value of g using any input-output pair. Using the first pair: 1 + g = 22 g = 22 - 1 g = 21 Step 2: Verify g with other pairs (optional, but good for checking). 16 + 21 = 37 49 + 21 = 70 The value is: g=21 3. Write these phrases as expressions (write the unknown number as x): a) A number is decreased by the square of 4: x - 4^2 b) The product of 6 and a number is increased by 10: 6x + 10 c) A number divided by 3 is added to the square of that number: (x)/(3) + x^2 d) A number multiplied by 5 is subtracted from 25: 25 - 5x e) Half of a number is added to one third of that number: (x)/(2) + (x)/(3) f) 2 less than the product of a number and 8: 8x - 2 4. Think of a number. Add 5. Multiply the sum by 2. Subtract 1. Write an expression using x for the unknown. Find the value of this expression if x = 12.5. Step 1: Write the expression. Let the unknown number be x. Add 5: x + 5 Multiply the sum by 2: 2(x + 5) Subtract 1: 2(x + 5) - 1 The expression is: 2(x + 5) - 1 Step 2: Find the value of the expression when x = 12.5. 2(12.5 + 5) - 1 2(17.5) - 1 35 - 1 34 The value of the expression is: 34 5. Copy and complete the following table: Step 1: Calculate the output for the given input values. For x = -1: 3(-1) - 4 = -3 - 4 = -7 For x = 0: 3(0) - 4 = 0 - 4 = -4 For x = 3: 3(3) - 4 = 9 - 4 = 5 For x = 10: 3(10) - 4 = 30 - 4 = 26 Step 2: Find the input x when the output is 250. 3x - 4 = 250 3x = 250 + 4 3x = 254 x = (254)/(3) x = 84.67 (approximately) The completed table is: |c|c|c|c|c|c| Input (x) & -1 & 0 & 3 & 10 & (254)/(3) \\ Output (3x - 4) & -7 & -4 & 5 & 26 & 250 \\ 6. If a = 2, b = 6 and c = 5, find the values of these expressions: a) 3b - a 3(6) - 2 = 18 - 2 = 16 The value is: 16 b) 3(b - a) 3(6 - 2) = 3(4) = 12 The value is: 12 c) a + b - c 2 + 6 - 5 = 8 - 5 = 3 The value is: 3 d) 4b - 2c 4(6) - 2(5) = 24 - 10 = 14 The value is: 14 7. Write an expression to describe the relationship of the data in the tables: a) Observe the relationship between m and n: 7 - 5 = 2 10 - 8 = 2 14 - 12 = 2 19 - 17 = 2 The output n is always 2 more than the input m. The expression is: n = m + 2 b) Observe the relationship between x and y: For x = -1, y = -2 y = 2x For x = -4, y = -8 y = 2x For x = -8, y = -16 y = 2x For x = -16, y = -40 y = 2.5x The relationship y = 2x holds for the first three pairs. Assuming there might be a typo in the last value of y (it should be -32 for y=2x to hold), the most consistent expression for the majority of the data is: y = 2x 8. What number doubled and added to 12 gives 20? Step 1: Set up the equation. Let the number be x. 2x + 12 = 20 Step 2: Solve for x. 2x = 20 - 12 2x = 8 x = (8)/(2) x = 4 The number is: 4 Send me the next one 📸

Write these word problems in mathematical language (without working out the answers): a) the difference between 69 and 43 b) the sum of 112 and 28 c) one third of 24 increased by 8 d) the square root of 16 is equal to the square of 2 e) 15 less than 99 f) 20 more than 16.

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Write these word problems in mathematical language (without working out the answers): a) the difference between 69 and 43 b) the sum of 112 and 28 c) one third of 24 increased by 8 d) the square root of 16 is equal to the square of 2 e) 15 less than 99 f) 20 more than 16.

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