The ratio of Toby's salary to George's salary is 13:8. The ratio of George's salary to Bill's salary is 2:3.
Find the ratio of Toby's salary to Bill's salary, and Bill's salary to total salary.
t:g = 13:8
g:b = 2:3 = 8:12
t:g:b = 13:8:12
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In January the value of stock increased by 25%,and in February ,it decreased by 20%.How did the value of the stock at the end of february compare with its value at the beginning of January?
To find the ratio of Toby's salary to Bill's salary:
Step 1: Determine the value of George's salary in terms of Toby's salary.
- Since the ratio of Toby's salary to George's salary is 13:8, we can set up the equation 13x = 8y, where x represents Toby's salary and y represents George's salary.
- To make it easier, we can simplify the equation by dividing both sides by 8. This gives us 13x/8 = y.
Step 2: Determine the value of Bill's salary in terms of George's salary.
- Since the ratio of George's salary to Bill's salary is 2:3, we can set up the equation 2y = 3z, where z represents Bill's salary.
- To make it easier, we can simplify the equation by dividing both sides by 2. This gives us 2y/2 = 3z/2. Simplifying further, we get y = (3/2)z.
Step 3: Find the ratio of Toby's salary to Bill's salary.
- By substituting the value of y from step 1 into the equation from step 2, we get 13x/8 = (3/2)z.
- Simplify the equation by multiplying both sides by 8/13, which gives us x = (24/13)z. Thus, the ratio of Toby's salary to Bill's salary is 24:13.
To find the ratio of Bill's salary to the total salary:
Step 4: Determine the value of the total salary in terms of Bill's salary.
- Since the ratio of George's salary to Bill's salary is 2:3, we can set up the equation 2y = 3z, where y represents George's salary and z represents Bill's salary.
- By solving the equation for y, we get y = (3/2)z.
Step 5: Determine the value of the total salary in terms of Toby's salary.
- By substituting the value of y from step 1 into the equation from step 4, we get (3/2)z = (3/2)(13x/8).
- Simplify the equation, which gives us (3/2)z = (39/16)x.
Step 6: Find the ratio of Bill's salary to the total salary.
- By dividing the equation from step 4 by the equation from step 5, we get (3/2)z / (39/16)x.
- Simplifying further, we get (3/2)z * (16/39)x = (48/39)x.
- Thus, the ratio of Bill's salary to the total salary is 48:39, which can be further simplified to 16:13.