Question

Maia had 2064 more beads than Jenny. After Maia used 144 beads to make a necklace, she had 5 times as many beads as Jenny. A) how many more beads did Maia have than Jenny in the end? How many beads did Maia have at first?

Answer 1

A) 1920 beads.

B) 2544 beads.

Explanation:

Let x represent the number of beads Jenny had and y represent the number of beads Maia had.

We have been given that Maia had 2064 more beads than Jenny. We can represent this information in an equation as:

`y=x+2064...(1)`

We are also told that After Maia used 144 beads to make a necklace, she had 5 times as many beads as Jenny.

We can represent this information in an equation as:

`y-144=5x...(2)`

A) As Maia had 2064 more beads than Jenny at first and she used 144 beads,so to get the number of beads Maia had in the end we will subtract 144 from 2064.

`\text{Number of beads Maia had more than Jenny in the end}=2064-144`

`\text{Number of beads Maia had more than Jenny in the end}=1920`

Therefore, Maia had 1920 more beads than Jenny in the end.

B) We will use substitution method to solve system of linear equations.

Upon substituting equation (1) in equation (2) we will get,

`x+2064-144=5x`

`x+1920=5x`

`x-x+1920=5x-x`

`1920=4x`

Let us divide both sides of our equation by 4.

`(1920)/(4)=(4x)/(4)`

`480=x`

Let us solve for y by substituting x=480 in equation (1).

`y=480+2064`

`y=2544`

Therefore, Maia had 2544 beads at first.