Let the width of the garden be $w$ meters. The length of the garden is given as $l = w + 7$.

The formula for the perimeter $P$ of a rectangle is: $P = 2(l + w)$

We are given that $P = 70$, so: $2(l + w) = 70$

Substitute $l = w + 7$ into the equation: $2((w + 7) + w) = 70$

Simplify: $2(2w + 7) = 70$

Divide through by 2: $2w + 7 = 35$

Solve for $w$: $2w = 35 - 7$ $2w = 28$ $w = 14$

Final Answer:

The width of the garden is 14 meters.

Let me know if you would like further clarification! Here are 5 related questions:

1. What is the length of the garden in this case?
2. How would the solution change if the perimeter was 80 meters?
3. Can you find the area of the garden with these dimensions?
4. How can this problem be expressed graphically?
5. What if the relationship was $l = 2w$? How would you solve for $w$?

Tip: Always double-check your equations and units to ensure accuracy when solving real-world problems!