I am sorry I didn't complete the problem
Here is the question:
Doris invested some money at 7% and some money at 8%. She invested $6,000 more at 8% than she did at 7%. Her yearly total from the two investments was $7.80. How much did Doris invest at each rate?
(A)$2,000 at7% and $8,000 at 8%
(B)$3,000 at 7% and $7,000 at 8%
(C)$1,500 at 7% and $9,000 at 8%
(D)$4,000 At 7% and $4,000 at 8%
if x at 7%, then
.07x + .08(x+6000) = 7.80
Fix the interest amount and solve for x. And pay more attention to what you type.
To solve this problem, we can set up a system of equations. Let's denote the amount of money Doris invested at 7% as x, and the amount she invested at 8% as x + $6,000 (since she invested $6,000 more at 8% than at 7%).
The equation for the yearly earnings from the investments can be expressed as:
0.07x + 0.08(x + $6,000) = $7,800
Now let's solve the equation:
0.07x + 0.08x + 0.08($6,000) = $7,800
Combining like terms:
0.15x + 0.08($6,000) = $7,800
Simplifying:
0.15x + $480 = $7,800
Subtracting $480 from both sides of the equation:
0.15x = $7,800 - $480
0.15x = $7,320
Dividing both sides of the equation by 0.15:
x = $7,320 / 0.15
x ≈ $48,800
So, Doris invested approximately $48,800 at 7% and $48,800 + $6,000 = $54,800 at 8%.
To determine which answer choice matches our calculations, we need to check if the invested amounts in each option satisfy the condition.
Let's calculate the total earnings for option (A):
($48,800 * 0.07) + ($54,800 * 0.08) = $7,836
Since this total is higher than $7,800, option (A) is not the correct answer.
Now let's calculate the total earnings for option (B):
($3,000 * 0.07) + ($7,000 * 0.08) = $610
Since this total is lower than $7,800, option (B) is not the correct answer.
Now let's calculate the total earnings for option (C):
($1,500 * 0.07) + ($9,000 * 0.08) = $760.50
Since this total is lower than $7,800, option (C) is not the correct answer.
Now let's calculate the total earnings for option (D):
($4,000 * 0.07) + ($4,000 * 0.08) = $520
Since this total is lower than $7,800, option (D) is not the correct answer.
Therefore, the correct answer is option (A) $2,000 at 7% and $8,000 at 8%.