Cheryl and Sally have some money in their wallets.If Cheryl puts 80 cents into her wallet, she will have 80% as much money as Sally.If instead,Sally puts 70 cents into her wallet, she will have 50% more money than Cheryl.How much money does each of them have.
Not clear if the new monies are transferred from the other person's wallet, or if they are new monies.
e.g. Do the 80 cents that Cheryl puts in her wallet come from Sally?
Please clarify.
If they start with amounts c and s (in cents), then we are told
c+80 = 0.80s
s+70 = 1.50c
now just solve for c and s.
To solve this problem, we need to set up and solve a system of equations based on the given information.
Let's assume Cheryl has x amount of money in her wallet, and Sally has y amount of money in her wallet.
According to the first statement, if Cheryl puts 80 cents into her wallet, she will have 80% as much money as Sally. This can be written as:
x + 0.80 = 0.8y
Now, let's consider the second statement. If Sally puts 70 cents into her wallet, she will have 50% more money than Cheryl. This can be written as:
y + 0.70 = 1.50(x)
We now have a system of two equations. Let's solve it.
1) x + 0.80 = 0.8y
2) y + 0.70 = 1.50(x)
To make the calculation easier, we can multiply both sides of equation 1) by 10 to get rid of the decimals:
10(x + 0.80) = 10(0.8y)
10x + 8 = 8y
Now, let's substitute this equation into equation 2):
8y + 0.70 = 1.50(x)
8(10x + 8)/10 + 0.70 = 1.50x
80x + 64 + 7 = 15x
80x - 15x = -71
65x = -71
x = -71/65
Now that we have the value of x (Cheryl's money), we can substitute it back into equation 1) to find y (Sally's money):
x + 0.80 = 0.8y
(-71/65) + 0.80 = 0.8y
Multiply both sides by 65 to get rid of the fraction:
-71 + 52 = 52y
-19 = 52y
y = -19/52
So, Cheryl has -(71/65) money in her wallet (which is approximately -1.0923) and Sally has -(19/52) money in her wallet (which is approximately -0.3654).
It's important to note that these results are negative, which suggests that both Cheryl and Sally owe money. However, it's unlikely for people to have negative money in their wallets in a realistic scenario. Double-check the information provided or the calculations to ensure accurate results.