Question

1. A truck driver drove 459 miles more this week than she did last week. If this is a percent change of 34%, how many miles did she drive last week?

a. 1,459 mi

b. 1,809 mi

c. 891 mi

d. 1,350 mi

Answer 1

Answer: D (1,350mi)

Explanation:

We can set up the equation to represent the percent change as follows:

Change in miles over original miles = 34 over 100

Substituting the given values, we get:

459 over x (as a fraction) = 34 over 100 (as a fraction)

To solve for x we can cross multiply:

459 x 100 = x x 34
45900 = 34x

Now, divide both sides by 34:

x = 45900 over 34 (as a fraction)
x = 1350
So, she drove approximately 1350 miles last week.

Therefore, the correct answer is:

d. 1,350 mi

Answer 2

Answer:

(d) 1,350 mi

Step-by-step explanation:

Let's denote the number of miles the truck driver drove last week as $x$.

According to the given information:

• The truck driver drove 459 miles more this week than she did last week.

This implies that this week's distance is $x + 459$.

• This increase in distance is a 34% change from last week's distance.

$x + 34\% \textsf{ of } x = x + 0.34x = 1.34x$

Since distance traveled this week is equal to an increase in distance, So, we can set up the equation:

$x + 459 = 1.34x$

Subtract $x$ from both sides:

$x + 459 -x= 1.34x-x$

$459 = 0.34x$

Now, divide both sides by $0.34$:

$x = \dfrac{459}{0.34}$

$x \approx 1350$

So, the truck driver drove approximately 1350 miles last week.

Therefore, the correct answer is option (d) 1,350 mi.