Word problems questions with answers

Questions

1. Question 1Consecutive numbers

   The sum of three consecutive even numbers is $120$. Find the smallest number.

   Show the worked solution

   1. Step 1: Let the smallest number be x. Write the other numbers in terms of x$x + 2$$x + 4$
   2. Step 2: Add them up and simplify$3x + 6 = 120$
   3. Step 3: Solve$3x = 114$$x = 38$
2. Question 2Ages

   Wei Jie's mother is $3$ times as old as Wei Jie. The sum of their ages is $36$ years. Find the mother's age.

   Show the worked solution

   1. Step 1: Let the child's age be x years. The mother's age is$3x$
   2. Step 2: Their ages add up to the total$4x = 36$
   3. Step 3: Solve$x = 9$
   4. Step 4: Answer the question asked$\text{Mother's age} = 27$
3. Question 3Perimeter

   The length of the rectangle is $5$ times its width. Its perimeter is $84$ cm. Find its area.

   Show the worked solution

   1. Step 1: Let the width be x cm. The length is$5x$
   2. Step 2: Perimeter = 2 × (length + width)$2(5x + x) = 84$$12x = 84$
   3. Step 3: Solve$x = 7$
   4. Step 4: Area = length × width$\mathstrut 35 \times 7 =$ $245$ cm²
4. Question 4Money

   A tin has some 20-cent coins and $2$ more 50-cent coins than 20-cent coins. The coins are worth $14.30 altogether. Find the number of 20-cent coins.

   Show the worked solution

   1. Step 1: Let the number of 20-cent coins be x. Work in cents$20x + 50(x + 2) = 1430$
   2. Step 2: Expand and simplify$70x + 100 = 1430$
   3. Step 3: Solve$70x = 1330$$x = 19$
5. Question 5Two-digit numbers: the digits reversed

   The tens digit of a two-digit number is $2$ times its ones digit. The number is $9$ more than the number formed by reversing its digits. Let the ones digit be $x$. Form an equation in $x$, and hence find the number.

   Show the worked solution

   1. Step 1: The ones digit is x. The tens digit is$2x$
   2. Step 2: The number = 10 × (tens digit) + (ones digit)$10(2x) + x$$= 21x$
   3. Step 3: Reversed, the digits swap places: 10 × (ones digit) + (tens digit)$10x + 2x$$= 12x$
   4. Step 4: The number − the reversed number = the difference: simplify$21x - 12x = 9$, so $9x = 9$
   5. Step 5: Solve$9x = 9$$x = 1$
   6. Step 6: The number: put x into the expression for it$\text{Number} = 21$
6. Question 6Rates: rate × time is the same amount

   A new printer prints a report at a rate of $17$ pages per minute. An old printer prints $6$ pages per minute and takes $11$ minutes longer to print the same report. Let the time taken by the new printer be $x$ minutes. Form an equation in $x$, and hence find the number of pages in the report.

   Show the worked solution

   1. Step 1: Amount = rate × time. In pages, the first time, and the second time (d minutes longer)$17x$$6(x + 11)$
   2. Step 2: The amounts are the same: the equation$17x = 6(x + 11)$
   3. Step 3: Expand, then collect the x terms on one side$17x - 6x = 66$, so $11x = 66$
   4. Step 4: Solve$x = 6$
   5. Step 5: The number of pages = 17 × x$\text{Pages} = 102$ pages