Chris's convertible gets gas mileage that is 40 percent greater than that of Stan's SUV. If Harry's hatchback gets gas mileage that is 15 percent greater than Chris's convertible, then Harry's hatchback gets what percent greater gas mileage than that of Stan's SUV?
Answer (1)
Let S be Stan's SUV gas mileage, then Chris's gas mileage is C = 1.40 S .
Harry's gas mileage is H = 1.15 C .
Substituting C = 1.40 S into the equation for H , we get H = 1.15 ( 1.40 S ) = 1.61 S .
The percentage increase is S H − S × 100 = S 1.61 S − S × 100 = 61% . Therefore, Harry's hatchback is 61% greater than that of Stan's SUV.
Explanation
Setting up the problem Let's break down this problem step by step to find out how much greater Harry's hatchback gas mileage is compared to Stan's SUV. We'll start by assigning variables to each car's gas mileage.
Finding Chris's gas mileage Let's say Stan's SUV gas mileage is represented by S . Chris's Convertible gets 40% better mileage than Stan's SUV, so Chris's gas mileage, C , can be expressed as: C = S + 0.40 S = 1.40 S
Finding Harry's gas mileage Harry's hatchback gets 15% better mileage than Chris's Convertible. So, Harry's gas mileage, H , can be expressed as: H = C + 0.15 C = 1.15 C
Expressing Harry's gas mileage in terms of Stan's Now, we want to express Harry's gas mileage in terms of Stan's gas mileage, S . We can substitute the expression for C from Step 2 into the equation for H from Step 3: H = 1.15 ( 1.40 S ) H = 1.61 S
Calculating the percentage increase To find the percentage by which Harry's gas mileage is greater than Stan's, we calculate the difference between their gas mileages, divide by Stan's gas mileage, and multiply by 100: Percentage increase = S H − S × 100 Substituting H = 1.61 S :
Percentage increase = S 1.61 S − S × 100 Percentage increase = S 0.61 S × 100 Percentage increase = 0.61 × 100 = 61% Therefore, Harry's hatchback gets approximately 61% greater gas mileage than Stan's SUV.
Final Answer So, Harry's hatchback gets approximately 61% greater gas mileage than Stan's SUV.
Examples
Imagine you're comparing the fuel efficiency of different car models to decide which one to buy. Knowing that one car gets 40% better mileage than another, and a third car gets 15% better mileage than the second, you can calculate the overall percentage improvement from the first car to the third. This helps you make an informed decision based on fuel savings and environmental impact. Understanding percentage increases is crucial in many real-life scenarios, from finance to health, allowing for better decision-making and planning.
