I have two questions that I need help with.

J

JaxJags

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I am having trouble starting and solving these two problems.

1.If Ben invests $2,000 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5 % of the total amount he invests?

Ben's second investment: $__________ at 5.5%.

I know that 4% of $2000 dollars would be $80. But, I am having trouble coming up with variables to form an equation to solve the problem.

2. What quantity of a 50% acid solution must be mixed with a 20% solution to produce 150 mL of a 40% solution?

_________ mL of 50% solution must be added.

I tend to have trouble with mixture problems, and I can't even find a way to start to solve this problem.



Thanks in advance to everyone who helps me. :D
 
JaxJags said:
I am having trouble starting and solving these two problems.

1.If Ben invests $2,000 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5 % of the total amount he invests?
Unknown

Money invested at 5.5% = F

Total money invested = 2000 + F[/color]

interest he receives each year is 4.5 % of the total amount he invests

What is the amount of interest he receives? = 0.045 * (2000 + F)

Now continue....


Ben's second investment: $__________ at 5.5%.[/color]

I know that 4% of $2000 dollars would be $80. But, I am having trouble coming up with variables to form an equation to solve the problem.

2. What quantity of a 50% acid solution must be mixed with a 20% solution to produce 150 mL of a 40% solution?

_________ mL of 50% solution must be added.

I tend to have trouble with mixture problems, and I can't even find a way to start to solve this problem.



Thanks in advance to everyone who helps me. :D
Click to expand...
 
So I just solve for F?

Would I equal this equation to 0?

0.045 * (2000 + F)= 0

Distribute .045 to (2000 + F)

90 + .045F = 0

Subtract 90 from both sides.

.045F = -90

F= -2000


I don't not what I did wrong.
 
JaxJags said:
So I just solve for F?

Would I equal this equation to 0? << Why would set that equal to 0? What statement/s in the problem guided you to do so?

Please read my previous response carefully.

0.045 * (2000 + F)= 0 <<< Incorrect

Distribute .045 to (2000 + F)

90 + .045F = 0

Subtract 90 from both sides.

.045F = -90

F= -2000


I don't not what I did wrong.
Click to expand...
 
I'm sorry, I'm am very confused. I can't seem to figure out what to equal the equation to.
 
I wrote:

What is the amount of interest he receives? = 0.045 * (2000 + F)
 
I wrote:

What is the amount of interest he receives? = 0.045 * (2000 + F)

This would also be equal to:

0.04 * 2000 + 0.055 * F

then we have:

0.04 * 2000 + 0.055 * F = 0.045 * (2000 + F)

Now solve for 'F'
 
Subhotosh Khan said:
I wrote:

What is the amount of interest he receives? = 0.045 * (2000 + F)

This would also be equal to:

0.04 * 2000 + 0.055 * F

then we have:

0.04 * 2000 + 0.055 * F = 0.045 * (2000 + F)

Now solve for 'F'
Click to expand...

Thank you so much! I get it now. Sorry for not getting it earlier and probably annoying you.

Thank you so much though. :D
 
So where are you with the second problem?

2. What quantity of a 50% acid solution must be mixed with a 20% solution to produce 150 mL of a 40% solution?
Click to expand...

Start with:

Unknown

amount of 50% acid concentration = x mL

Amount of acid "x" mL 50% solution = 0.5 * x.......................................................(1)

amount of 20% acid concentration = (150-x) mL

Amount of acid "(150-x)" mL 20% solution = 0.2 * (150-x)........................................(2) [edited]

amount of Acid in 150 mL 40% solution = 150 * 0.4........................................(3)

The amount of acid must be same ? (1) + (2) = (3)

Now continue...
 
So would the answer be 86 mL?

50% of 86 = 43
20% of 86 = 17.2

43 + 17.2 = 60.2

40% of 150 = 60
 
JaxJags said:
So would the answer be 86 mL? <<<<< No - that is incorrect. Follow the outline of solution I provided you.

50% of 86 = 43
20% of 86 = 17.2

(86 + 86) does not equal to 150
43 + 17.2 = 60.2

40% of 150 = 60
Click to expand...
 
So it would be 100mL of the 50% solution mixed with 50mL of the 20% solution.
 
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