# The mean of Susan's math and science scores is 74 points. The mean of her math and English scores is 83 points. How many more points did Susan score in English than in science?

m+s = 148

(m + e )/2 = 83
m+ e = 166

subtract them:

e - s = 18

## Let's assume Susan's math score is represented by M, her science score by S, and her English score by E.

According to the given information:
(M + S) / 2 = 74 (Mean of math and science scores is 74)
(M + E) / 2 = 83 (Mean of math and English scores is 83)

To solve this problem, we need to eliminate the fractions by multiplying both equations by 2:
2(M + S) / 2 = 2 * 74
2(M + E) / 2 = 2 * 83

Simplifying the equations:
M + S = 148
M + E = 166

To find how many more points Susan scored in English than in science, we subtract the equation M + S from the equation M + E:
(M + E) - (M + S) = 166 - 148
M - M + E - S = 18
E - S = 18

Therefore, Susan scored 18 more points in English than in science.

## To determine how many more points Susan scored in English than in science, we need to find the scores for both subjects individually.

Let's assume Susan scored x points in math, y points in science, and z points in English.

We are given that the mean (average) of Susan's math and science scores is 74 points, which means the sum of her math and science scores is 2 times the mean. Therefore, we have:

x + y = 2 * 74
x + y = 148

Similarly, the mean of Susan's math and English scores is 83 points, which means the sum of her math and English scores is 2 times the mean. Therefore, we have:

x + z = 2 * 83
x + z = 166

Now we have a system of two equations:

x + y = 148
x + z = 166

We can solve this system to find the values of x, y, and z. Subtracting the first equation from the second equation, we get:

(x + z) - (x + y) = 166 - 148
x + z - x - y = 18
z - y = 18

So, Susan scored 18 more points in English (z) than in science (y).