A bakery is making a cake for a customer who wants it to be decorated with a specific pattern.the customer provide a design in binary code 101101. The baker only understand the code as quinary number.the baker had already made 45cakes in the morning and 12cakes in the afternoon before the customer came to him,he plans to divide the cake in the largest number of equal slices but unfortunately found a number 120 on the screen which made him to wonder which two numbers he could have pressed to get the number Help the baker to write down the code he can use in the design and also determine the number of slices each cake will be made off and also find which two set of number do you think the baker could have pressed in the calculator to get number on the screen
This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Let's help the baker with these puzzles!
1. Code for the design (Binary to Quinary conversion)
The customer's design is in binary code: 101101₂.
The baker understands quinary numbers (base 5).
Step 1: Convert the binary number to a decimal (base 10) number.
101101₂ = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)
= (1 × 32) + (0 × 16) + (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1)
= 32 + 0 + 8 + 4 + 0 + 1
= 45₁₀
Step 2: Convert the decimal number to a quinary (base 5) number.
Divide 45 by 5 and note the remainders:
45 ÷ 5 = 9 remainder 0
9 ÷ 5 = 1 remainder 4
1 ÷ 5 = 0 remainder 1
Reading the remainders from bottom to top, the quinary number is 140₅.
The code the baker can use in the design is 140₅.
2. Number of slices each cake will be made of
The baker made 45 cakes in the morning and 12 cakes in the afternoon. He wants to divide each cake into the largest number of equal slices. To find the largest number of equal slices that can be made from each cake, we need to find the Greatest Common Divisor (GCD) of the numbers 45 and 12.
Step 1: Find the factors of 45.
Factors of 45: 1, 3, 5, 9, 15, 45
Step 2: Find the factors of 12.
Factors of 12: 1, 2, 3, 4, 6, 12
Step 3: Identify the greatest common factor.
The common factors are 1 and 3. The greatest common factor is 3.
Each cake will be made of 3 slices.
3. Two numbers the baker could have pressed to get 120
The baker saw the number 120 on the screen, likely from a multiplication. We need to find pairs of numbers that multiply to 120. These are the factors of 120.
Here are some pairs of numbers the baker could have pressed:
1 and 120
2 and 60
3 and 40
4 and 30
5 and 24
6 and 20
8 and 15
10 and 12
That's 5 down. Send the next one.