Answer:
-$1000
Step-by-step explanation:
(3800 - x)*3.5/100 = (3800 + x)*6/100
(3800 - x)7/200 = 3/50(3800 + x)
3800 - x = 12/7(3800 + x)
3800 - x = 45600/7 + 12x/7
(19x + 19000)/7 = 0
19x = -19000
x = -$1000.
The minus implies that the investment must occur in the first account, not the second. It wouldn't make sense to add more money into the second account, because the second account already exceeds the $188 interest with the amount it has in there. Therefore $1000 must be added from the second account and invested into the first.
To find this answer, we should subtract 2 1/2 from 3 1/4. The simplest way to do this is to turn them into improper fractions, found the least common denominator, and subtract the numerators.
3 1/4=13/4
2 1/2=5/2
The least common multiple is 4, so we should multiply the numerator and denominator of 5/2 by 2.
5/2=10/4
Now we can just subtract the numerators.
13/4-10/4=3/4
Using the math above, we can see that it saves D. 3/4 hours.
Change the percentage into a decimal and multiply for the answer.
$80,000 * .025 = $2,000
Since interest=investment*interest rate*time in years for simple interest, we know that there are 2 separate investments. If the amount invested at 6% simple interest is x dollars and the amount invested at 8% is y dollars, then we know that x+y=6000 since she spent all 6000 dollars on only 2 separate investments. Subtracting y from both sides, we get that 6000-y=x. In addition, we know that her interest for the 6% interest rate is x*0.06*1 as well as y*0.08*1 for the 8% simple interest. Since the total interest is 410$, we know that x*0.06*1+y*0.08*1=410. Since y=6000-x, we plug that in to get x*0.06+(6000-x)*0.08=410. Using the distributive property to expand, we get x*0.06+480-0.08x=410=-0.02*x+480. Subtracting 480 from both sides, we get -0.02*x=-70. After that, we can multiply both sides by -50 (since -0.02 times -50 is 1) to get x=3500=amount invested at 6%. Since the amount invested at 8% is 6000-x, that equals 6000-3500=2500
