Two business partners, Ellen and Bob, invested money in their business at a ratio of 6 to 7. Bob invested the greater amount. The total amount invested was $260. How much did each partner invest?
120 and 140
We could get the answer a couple of ways. I divided 260 by 13 to get 20. Then I multiplied the parts of the ratio by 20.
or, using algebra
let the two amounts invested by 6x and 7x
(notice 6x : 7x = 6 : 7 )
then 6x + 7x = 260
13x = 260
x = 20
then 6x = 6(20) = 120
and 7x = 7(20) = 140
the same answers obtained by Ms Sue
Ellen and Bob invested money in their business at a ratio of 7 to 9. Bob invested a greater amount. The total amount invested was $320. How much did each partner invest?
To solve this problem, we can start by assigning variables to the amounts invested by Ellen and Bob.
Let's say Ellen invested x dollars, and Bob invested y dollars.
According to the given information, the ratio of their investments is 6 to 7, meaning the ratio of Ellen's investment to Bob's investment is 6/7.
Now, we can set up a proportion to solve for y:
x/y = 6/7
To eliminate the fraction, we can cross-multiply:
7x = 6y
Next, we know that the total amount invested by both partners is $260. So we can set up another equation:
x + y = 260
Now we have a system of two equations:
7x = 6y (equation 1)
x + y = 260 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination. I will solve it using the substitution method:
Using equation 1, we can solve it for x in terms of y:
7x = 6y
x = (6/7)y
Now, substitute this value of x into equation 2:
(6/7)y + y = 260
Multiply through by 7 to get rid of the fraction:
6y + 7y = 1820
Combine like terms:
13y = 1820
Divide both sides by 13:
y = 140
Bob invested $140.
Now, substitute this value of y back into equation 2 to find x:
x + 140 = 260
x = 120
Ellen invested $120.
Therefore, Ellen invested $120 and Bob invested $140.