The ratio of the number of alex's beads to the number of betty's beads was 3:4.after alex bought another 72 beads,the ratio became became 3:1.
A. How many beads did betty have?
B.if alex gave away 80 beads,what would by the new ratio of the number of betty's beads to the number of alex's beads?
How do you do the part B.?
a/b = 3/4
(a+72)/b = 3/1
or, more managabely
3b = 4a = a+72
a = 24 so b = 32
solve for a and b, and then for the 2nd part,
(a+72-80)/b = 16/32 = 1/2
To solve part B, we need to use the given information that after Alex bought another 72 beads, the ratio of their beads became 3:1. From this, we can deduce that:
3x + 72 = x
Let's solve for x.
3x - x = -72
2x = -72
x = -36
Since we cannot have a negative number for the number of beads, it means that there is no solution to the problem. Hence, we cannot find the new ratio of the number of Betty's beads to the number of Alex's beads if Alex gave away 80 beads.
To find the answer to part B, we first need to determine the number of beads Betty initially had in part A.
Let's denote the initial number of Alex's beads as 3x and the initial number of Betty's beads as 4x.
According to the information given, after Alex bought another 72 beads, the new ratio became 3:1. This means that Alex now has 3x + 72 beads and Betty has 4x beads.
Since the new ratio is 3:1, we can set up the following equation:
(3x + 72) / 4x = 3/1
Now, we can solve for x:
3(3x + 72) = 4x
9x + 216 = 4x
5x = -216
x = -43.2
The negative value for x does not make sense in this context, so we can conclude that there was an error in the given information or the problem itself.
Without the correct value of x, we cannot proceed to find the number of Betty's initial beads or determine the new ratio in part B.