Question

A total of m matches are needed to fill 30 matchboxes with the same number of matches in each box. How many matches are in each box?

If each box has three matchsticks less, there will be enough sticks for 32 boxes. What is the value of m?

Answer 1

To find the number of matches in each box, we can set up and solve two equations using the given information. The value of m is equal to 45.

Step-by-step explanation:

To find the number of matches in each box, we can set up the equation: m matches / 30 boxes = x matches per box. Solving for x, we have x = m/30.

Next, we can use the second statement to set up another equation: (m - 3) matches / 32 boxes = x matches per box. Solving for x, we have x = (m - 3)/32.

Setting the two equations equal to each other, we get: m/30 = (m - 3)/32. Cross-multiplying and simplifying, we have 32m = 30(m - 3), which simplifies to 2m = 90. Therefore, m = 45.