Number of beads she have is 62 .
<u>Step-by-step explanation:</u>
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:
<u>when she makes them into groups of 9, 8 beads are left out </u> equation is
<u>when she groups into groups of 8 , 6 beads are left out</u>, equation is

Equating both equation's we get:
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⇒ 
By hit & trial method , we put x = 6 & y=7:
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Since , LHS = RHS x = 6 & y=7 satisfies the equation
. So putting value of x=6 in
we get:
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Therefore, Number of beads she have is 62 .