Question

Niel has a bucket of beads. He uses them to make 8 identical necklaces and then buys 25 beads at the store. He ends up with a total of 500 beads. How many did he start with? Identify
the operations needed to solve this problem using the equation + 25 = 500 (1 point)

Answer 1

A window cleaner has enough supplies to clean 21 windows per office building on a certain number of buildings. They can also clean the windows of a school with 42 windows. Altogether, there are enough supplies to clean 126 windows. How many office buildings can be wasned?
Identify the equation that would be used to solve this problem algebraically. (1 point)

Answer 2

Let x be the number of beads Niel started with.

Given that he used the beads to make 8 necklaces, each identical, he used a total of 8x beads.
After buying 25 more beads, the total number is 8x + 25.

Setting up the equation: 8x + 25 = 500

To solve the equation:
Subtract 25 from both sides: 8x = 475
Divide both sides by 8: x = 59.375 beads

Therefore, Niel started with 59.375 beads.

Answer 3

Let x be the number of office buildings.

The window cleaner has enough supplies to clean 21 windows per office building, so the total number of windows cleaned on the office buildings would be 21x. Additionally, they can clean the windows of a school with 42 windows. This adds 42 windows to the total count.

The total number of windows cleaned is given as 126, so we can set up the equation:

21x + 42 = 126

To solve this equation algebraically, we can simplify it to:

21x = 126 - 42
21x = 84
x = 84 / 21
x = 4

Therefore, the equation is:
21x + 42 = 126