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

Joyce has total 62 colored beads.

Step-by-step 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.

Number of beads she have is 62 .

Step-by-step 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

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

Equating both equation's we get:

⇒

⇒

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

⇒

⇒

⇒

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

⇒

⇒

⇒

Therefore, Number of beads she have is 62 .

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

what are ur choices?