Question

joyce has between 25 to 75 coloured beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, 6 beads are left out,how many beads are left

Answer 1

Number of beads she have is 62 .

Explanation:

Here we have , joyce has between 25 to 75 colored beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, We need to find how many beads are left . Let's solve this:

when she makes them into groups of 9, 8 beads are left out equation is

`9x+8`

when she groups into groups of 8 , 6 beads are left out, equation is

`8y+6`

Equating both equation's we get:

⇒
`9x+8 = 8y+6`

⇒
`9x-8y = -2`

By hit & trial method , we put x = 6 & y=7:

⇒
`9(6)-8(7) = -2`

⇒
`54-56= -2`

⇒
`-2= -2`

Since , LHS = RHS x = 6 & y=7 satisfies the equation
`9x+8 = 8y+6` . So putting value of x=6 in
`9x+8` we get:

⇒
`9x+8`

⇒
`54+8`

⇒
`62`

Therefore, Number of beads she have is 62 .

Answer 2

Joyce has total 62 colored beads.

Explanation:

For making groups of 9, let the number of beads be x.

total beads = 9x + 8

For making groups of 8, let the number of beads be y.

total beads = 8y + 6

As the total number of beads in both cases are same so,

9x + 8= 8y + 6

or, 9x-8y = -2

Now lets check the values through hit and trial;

First check; x=6, y=7

9*6 - 8*7 = -2

or, 54- 56 = -2

or, -2 =-2

This satisfies our equation.

Hence; Total beads = 9*6 + 8 = 62

The total number of beads joyce had is 62.