Strategies for solving multi-step real-world problems
A number is doubled and then increased by 5. The result is 17. What is the number?
Let x be the number: 2x + 5 = 17, so 2x = 12, x = 6
The sum of three consecutive integers is 48. What is the largest integer?
Let integers be x, x+1, x+2: x + (x+1) + (x+2) = 48, 3x + 3 = 48, 3x = 45, x = 15, largest = 17
A train travels 300 miles in 5 hours. How long will it take to travel 420 miles at the same speed?
Speed = 300 ÷ 5 = 60 mph, Time = 420 ÷ 60 = 7 hours
Solve the system: 2x + y = 11 and x - y = 4
Add the equations: 3x = 15, x = 5, then 5 - y = 4, so y = 1
A rectangle has length 8 and width 5. If both dimensions are increased by x, the new area is 80. Find x.
New dimensions: (8+x)(5+x) = 80, 40 + 13x + x² = 80, x² + 13x - 40 = 0, (x+15)(x-2) = 0, x = 2