1. The sum of the ages of James and Remy 5 years ago was 44. Twenty-two years from now, James' age will be 52 less than twice3 Remy's age then. Find their present ages.

2. Two numbers have a sum of 41. Their difference is 5. What are the numbers?

3. The perimeter of a football field is 320 yards. Its length measures 40 yd more than its width. Find the dimensions of the field.

(j-5) + (r-5) = 44

(j+22) + 52 = 2 (r+22)

j + r = 54
so
j = (54-r)
then
(54 - r + 22) + 52 = 2 r + 44
128-r = 2 r + 44
3 r = 84
r = 28
j = 26
=================================
x and (41-x)
(41-x) - x = 5
etc
=========================
2 L + 2 W = 320
W = (L-40)
so
L + (L-40) = 160
etc

(j-5) + (r-5) = 44

(j+22) + 52 = 2 (r+22)

j + r = 54
so
j = (54-r)
then
(54 - r + 22) + 52 = 2 r + 44
128-r = 2 r + 44
3 r = 84
r = 28
j = 26
=================================
x and (41-x)
(41-x) - x = 5
etc
=========================
2 L + 2 W = 320
W = (L-40)
so
L + (L-40) = 160
etc

1. To solve this problem, we can use a system of equations. Let's first assign variables to James' and Remy's present ages. Let's say James' age is J, and Remy's age is R.

According to the first statement, "The sum of the ages of James and Remy 5 years ago was 44", we can write an equation as follows:
(J-5) + (R-5) = 44

The second statement says, "Twenty-two years from now, James' age will be 52 less than twice Remy's age then." This can be expressed as:
(J+22) = 2(R+22) - 52

Now we have a system of two equations:
(J-5) + (R-5) = 44
(J+22) = 2(R+22) - 52

Simplifying the equations, we now have:
J + R = 54
J + 22 = 2R + 44 - 52

Rearranging the second equation, we have:
J - 2R = 30

Now we can solve this system of equations to find the values of J and R.

Next, we can use the elimination method to solve the system. Multiply the first equation by 2 to eliminate J:
2(J + R) = 2(54)
2J + 2R = 108

Now we can subtract the equation J - 2R = 30 from 2J + 2R = 108:
3J = 78
J = 26

Substituting the value of J into the first equation, we have:
26 + R = 54
R = 54 - 26
R = 28

Thus, James' present age is 26 and Remy's present age is 28.

2. To find the two numbers, we can set up a system of equations based on the given information.

Let's assume the larger number is A and the smaller number is B.

According to the statement, "Two numbers have a sum of 41," we can write the equation:
A + B = 41

The statement also says, "Their difference is 5," which can be written as:
A - B = 5

Now we have a system of equations:
A + B = 41
A - B = 5

To solve this system, we can use the elimination method by adding the two equations together:
(A + B) + (A - B) = 41 + 5
2A = 46
A = 46/2
A = 23

Substituting the value of A into the first equation, we have:
23 + B = 41
B = 41 - 23
B = 18

Thus, the two numbers are 23 and 18.

3. To solve this problem, we can assign variables to the length and width of the football field.

Let's say the length of the field is L and the width of the field is W.

According to the statement, "The perimeter of a football field is 320 yards," we can write the equation:
2L + 2W = 320

The statement also says, "Its length measures 40 yd more than its width," which can be expressed as:
L = W + 40

Now we have two equations:
2L + 2W = 320
L = W + 40

To solve this system, we can substitute the value of L from the second equation into the first equation:
2(W + 40) + 2W = 320
2W + 80 + 2W = 320
4W + 80 = 320
4W = 240
W = 240/4
W = 60

Substituting the value of W into the second equation, we have:
L = 60 + 40
L = 100

Thus, the dimensions of the football field are 100 yards by 60 yards.