If Joe invested $7000 at x% and $13,000 at 3% more, find x if the income from both investments is $1190
I'm thinking that the equation would r something like 1,190=(13,000)(.03) but please correct me if I'm wrong. Thank you for your assistance.
no, your equation doesn't even contain any variables.
x(7000) + (x+.03)(13000) = 1190
7000x + 13000x + 390 = 1190
20000x = 800
x = .04 or 4%
To solve this problem, we need to set up two equations - one for each investment - and then solve for the unknown interest rate, denoted as x%.
Let's start with the first investment of $7000 at x% interest. The income from this investment can be calculated by multiplying the amount invested by the interest rate expressed as a decimal:
Income from first investment = $7000 * (x/100)
Now, for the second investment of $13,000 at 3% more interest, we need to add 3% to the interest rate x%. This can be expressed as (x + 3)% and then converted to a decimal:
Income from second investment = $13,000 * ((x + 3)/100)
Since the total income from both investments is $1190, we can set up the equation:
$1190 = $7000 * (x/100) + $13,000 * ((x + 3)/100)
Now, let's solve this equation to find the value of x:
First, distribute the percentages:
$1190 = $7000 * (x/100) + $13,000 * (x/100 + 3/100)
Next, simplify the equation:
$1190 = $7000x/100 + $13,000x/100 + $390
Combine like terms:
1190 = 70x + 130x + 390
Combine the x terms:
1190 = 200x + 390
Subtract 390 from both sides:
800 = 200x
Divide both sides by 200:
x = 800/200
Simplify:
x = 4
Therefore, the interest rate for the first investment is 4%.