Question

А (b) Two ovens are used to bake banana cakes and chocolate cakes. Each oven will ding according to its setting time. A banana cake takes 50 minutes to bake wbile a chocolate cake takes 45 minutes to bake.

(i) If each cake is put into the ovens at the same time, what is the time taken until both ovens ding simultaneously?

(ii) When the both ovens ding, how many banana cakes and chocolate cakes are baked? ​

Answer 1

The ovens will ding simultaneously after 450 minutes, and by that time, 9 banana cakes and 10 chocolate cakes will have been baked.

Step-by-step explanation:

To solve this problem, we need to find the least common multiple (LCM) of the two baking times for the banana cakes and the chocolate cakes, which are 50 minutes and 45 minutes, respectively.

Step-by-step solution:

1. List the multiples of each number until we find a common multiple.
   
   • 50, 100, 150, 200, 250, 300 (and so on)
   • 45, 90, 135, 180, 225, 270, 315 (and so on)
2. Identify the smallest multiple that appears in both lists. This is the LCM. In this case, the LCM is 450 minutes.
3. The ovens will ding simultaneously after 450 minutes.

(ii) To find out how many banana cakes and chocolate cakes are baked when both ovens ding:

• Divide the LCM by the baking time for each type of cake.
• Banana cakes: 450 minutes ÷ 50 minutes = 9 cakes
• Chocolate cakes: 450 minutes ÷ 45 minutes = 10 cakes

When both ovens ding simultaneously, 9 banana cakes and 10 chocolate cakes are baked.

Answer 2

(b)(i) LCM of 45 and 50 = 450

Hence, it take 450 minutes until both ovens ding simultaneously.

(b)(ii) 450÷50=9 banana cakes baked

450÷45=10 chocolate cakes baked.