Answer:
1. Callum = 2; Eilidh = 17; Caitlin's =22.
2. Ewan = 44; tree = 308.
Explanation:
Q1. Callum, Eilidh, and Caitlin
Let x = Callum's age
y = Eilidh's age
z = Caitlin's age
We have three conditions.
(1) x = y - 5
(2) z = y + 15
(3) x + y + z = 31
Step 1. Eliminate one of the variables in two of the equations
Subtract (1) from (2): z - x = 20
Rearrange: (4) -x + z = 20
Solve (2) for y: (5) y = z - 15
Substitute into (3): x + z - 15 + z = 31
(6) x + 2z = 46
Step 2. Set up two new equations in two variables
(5) -x + z = 20
(6) x + 2z = 46
Add (5) and (6): 3z = 66
Divide each side by 2: z = 22
Step 3. Substitute z into (5)
-x + 22 = 20
x = 2
Step 4. Substitute x into (1)
2 = y - 5
Add 5 to each side y = 7
Callum's age is 2; Eilidh's age is 7; Caitlin's age is 22.
Q2. Ewan and the tree
Let x = Ewan's age
y = tree's age
We have two conditions.
(1) y = 7x
(2) x + y = 352
Rearrange (1) (3) -7x + y = 0
(2) x + y = 352
Subtract (3) from (2) 8x = 352
Divide each side by 8 x = 44
Substitute y into (1) y = 7 × 44
y = 308
Ewan's age is 44; the tree's age is 308.
