Wendy's savings to Stef's savings were 5:6. After they spent $28 each, then the ratio became 1:4.
A) Find Wendy's saving before spent $28.
B) What's Stef's saving after spent $28.
To solve this problem, let's denote Wendy's savings before spending $28 as "x" and Stef's savings before spending $28 as "y".
According to the problem, the ratio of Wendy's savings to Stef's savings before spending $28 is 5:6. This can be written as:
x/y = 5/6
After they both spent $28, the ratio of Wendy's savings to Stef's savings became 1:4. This can be written as:
(x - 28)/(y - 28) = 1/4
Now, let's solve the equations to find Wendy's savings before spending $28 (x) and Stef's savings after spending $28 (y).
Solving equation (1):
x/y = 5/6
Cross multiplying, we get:
6x = 5y
Simplifying, we have:
x = (5/6)y
Substituting this value of x into equation (2):
[(5/6)y - 28)/(y - 28) = 1/4
Now, we can solve equation (2) for y.
Cross multiplying, we get:
4(5y - 168) = (6)(y - 28)
Simplifying, we have:
20y - 672 = 6y - 168
Combining like terms, we get:
14y = 504
Dividing both sides by 14, we find:
y = 36
Now, substituting the value of y back into equation (1) to find x:
x = (5/6)(36)
x = 30
Therefore, Wendy's savings before spending $28 (x) was $30, and Stef's savings after spending $28 (y) is $36.
To solve this problem, let's break it down into smaller steps.
Step 1: Write the original ratio of Wendy's savings to Stef's savings.
The original ratio is given as 5:6.
Step 2: Determine the total ratio after they spent $28 each.
The total amount spent is $28 each. Since they both spent the same amount, we can subtract $28 from both sides of the ratio to get 5 - 28 : 6 - 28, which simplifies to -23: -22.
Step 3: Simplify the negative ratio.
We can simplify the negative ratio by multiplying both sides by -1 to change the signs: 23:22.
Step 4: Find the ratio when they have $1 left each.
Since we are given that the new ratio is 1:4, we can multiply both sides of the ratio by 23 to find the total amount each person has when they have $1 left. This gives us 23:92.
Step 5: Find the total amount each had before spending $28.
Since we know they had $1 left each, we can multiply both sides of the ratio by 28 to find the total amount each person had before spending $28. This gives us 28 * 23 : 28 * 92, which simplifies to 644:2,576.
Step 6: Calculate Wendy's savings before spending $28 (Part A).
Wendy's savings is given by the first number in the ratio 644:2,576. Therefore, Wendy's savings before spending $28 was $644.
Step 7: Calculate Stef's savings after spending $28 (Part B).
Since we originally had a ratio of 5:6, and they both spent $28 each, Stef's savings after spending $28 can be calculated by multiplying the second number of the original ratio by the ratio of what they have left over from Step 4. This gives us 6 * (92 / 23), which simplifies to 24.
Therefore, the answers to the questions are:
A) Wendy's savings before spending $28 was $644.
B) Stef's savings after spending $28 is $24.