Glenda, Hilda, and Inez have $35,000 invested in a business. Glenda's investment is one-half Hilda's and three times Inez's investment. How much does each person have invested?
Glenda's --- x
Hilda's ---- 2x
INez's ---- (1/3)x
x + 2x + x/3 = 35000
multiply each term by 3
3x + 6x + x = 105000
solve for x, etc
G + H + I = 35000
G = 1/2 H ... H = 2 G
G = 3 I ... I = G / 3
substituting ... G + 2G + G/3 = 35000
... 3G + 6G + G = 105000 ... G = 10500
substitute back to find H and I
To find out how much each person has invested, let's use variables to represent their investments.
Let's assume:
Glenda's investment = G
Hilda's investment = H
Inez's investment = I
From the given information, we have three equations:
1) Glenda's investment is one-half Hilda's investment:
G = 0.5H
2) Glenda's investment is three times Inez's investment:
G = 3I
3) The total investment of Glenda, Hilda, and Inez is $35,000:
G + H + I = $35,000
Now, we can solve these equations together:
Since G = 3I (from equation 2), we can substitute 3I in place of G in equation 1:
3I = 0.5H
Next, let's solve for H in terms of I:
H = 6I (multiplying both sides of the equation by 2)
Now we will substitute these values of G and H into equation 3:
(3I) + (6I) + I = 35,000
10I = 35,000
I = 35,000 / 10
I = 3,500
Thus, Inez has invested $3,500.
Now, substituting the value of I into the equations for G and H:
Glenda's investment (G) = 3I = 3(3,500) = $10,500
Hilda's investment (H) = 6I = 6(3,500) = $21,000
Therefore, Glenda has invested $10,500, Hilda has invested $21,000, and Inez has invested $3,500.