Question

Mandy wants to distribute some beads to her sisters. If she gives each sister 8 beads, she will have 11 beads left. If she gives each sister 12 beads, she will be short of 9 beads. How many beads does she have?

a) 31 beads
b) 41 beads
c) 51 beads
d) 61 beads

Answer 1

Mandy has 51 beads.

Step-by-step explanation:

To determine how many beads Mandy has, we can set up a system of equations based on the information given. Let's say Mandy has x beads. According to the first statement, if she gives each sister 8 beads, she will have 11 beads left. This can be represented as x - 8s = 11, where s is the number of sisters.

Similarly, the second statement states that if she gives each sister 12 beads, she will be short of 9 beads. This can be represented as x - 12s = -9. We can solve these two equations simultaneously to find the value of x, the number of beads Mandy has.

Let's multiply the first equation by 12 and the second equation by 8 to eliminate the 's' term. We get 12x - 96s = 132 and 8x - 96s = -72. Subtracting the second equation from the first gives us 4x = 204. Solving for x, we find that Mandy has 51 beads.