Final answer:
To find the number of single-door cupboards, two equations were set up and solved simultaneously. Using algebra, it was determined that there are 3 single-door cupboards in the kitchen.
Step-by-step explanation:
The question asked is a basic algebra problem involving determining the number of single-door cupboards when given the total number of cupboard doors and cupboards. To solve this problem, we can set up a system of equations where x represents the number of single-door cupboards and y represents the number of double-door cupboards. The first equation based on the total number of cupboards would be x + y = 9, and the second equation based on the total number of cupboard doors would be x + 2y = 15. Solving these two equations simultaneously gives us the solution to the problem.
Solving for x in x + y = 9, we get x = 9 - y. Substituting this into the second equation, x + 2y = 15, yields (9 - y) + 2y = 15. Solving for y gives us y = 6. Substituting y = 6 back into the first equation, we find that x = 9 - 6, so x = 3. Therefore, there are 3 single-door cupboards in the kitchen.