#1**0 **

Since the range is 10, the first and last scores must be different. And we only have 4 scores total. So in order for there to be a mode, and for that mode to be 44, it must be that the middle two scores are both 44 (just like you have already put )

Then let's let a be the first (lowest) score, and let d be the last (highest) score.

Since the mean is 45, we know:

(a + 44 + 44 + d) / 4 = 45

(a + 88 + d) / 4 = 45

Multiply both sides of the equation by 4

a + 88 + d = 180

Subtract 88 from both sides of the equation.

a + d = 92

Subtract d from both sides of the equation.

a = 92 - d

Since the range is 10, we know:

d - a = 10

Substitute 92 - d in for a

d - (92 - d) = 10

Distribute -1 to both terms in parenthesees

d - 92 + d = 10

Combine like terms

2d - 92 = 10

Add 92 to both sides

2d = 102

Divide both sides by 2

d = 51

Now we can find a using this value of d:

a = 92 - d

Substitute 51 in for d

a = 92 - 51

a = 41

hectictar Sep 21, 2020