James's weekly quiz scores are shown in the stem-and-leaf plot below.
if he drops his scores from the first two weeks, his mode score increases by $2$. how much would his mean score increase?

By 0.75

Step-by-step explanation:

From the stem-and-leaf plot you can find James's scores:

79, 81, 83, 83, 83, 85, 85, 88, 94, 99.

The mode is 83 (most often score). If he drops his scores from the first two weeks, his mode score increases by 2. This means that the mode became 85 and the data looks like

79, 81, 83, 85, 85, 88, 94, 99.

Now find two means.

1. The old mean:

2. The new mean:

Thus, the mean will increase by 0.75.

Let's write down what we know:

a=50+b

b=30+c

After one hour:

(a+50)*2=-70+3*(c+50)

let's eliminate the brackets:

2a+100=-70+3c+150
2a+100=+3c+80
which is:

2a=-20+3c
substituting from a=50+b:

100+2b=-20+3c

substituting from b=30+c

100+2(30+c)=-20+3c

100+60+2c=-20+3c

160+20=3c-2c

180=c.

So we know that c is equal to 40, then b will be b=30+c

b=30+180=210.

So B had 210 miles initially.