Henry has $15,000 to invest. He invests x dollars at 4% and the rest at 3.5%. Suppose at the end of the year Henry has $15,575. How much money did he start with in each account?

## word problem

# 3 Answers

PV1 = x

PV2 = 15000-x

r1=.04

r2=.035

FV = PV1(1+r1) + PV2(1+r2)

15575 = 1.04x + 1.035(15000-x)

15575 = 1.04x + 15525 - 1.035x

50 = .005x

x = $10,000 = PV1

$15,000-x = $5000 = PV2

This can be solved using a systems of equations approach, the system being two eqns with two unknowns. Te first eqn will represent the total amt of money in each acct, and the 2nd eqn will represent the interest earned in each acct.

Let x = amt invested in the 1st acct

Let y = amt invested in the second acct

The sum between the accts is 15,000, so

x + y = 15,000 (eqn 1)

The interest earned in acct 1 is 0.04x and in acct 2 is 0.035y, and the total interest earned is the sum of those two. In addition, we know the total interest earned to be equal to (15,575 - 15,000) = 575

I1 + I2 = 575

0.04x + 0.035y = 575 (eqn 2)

Solve by substitution. Solve for either variable in eqn 1 and substitute into eqn 2.

x = (15,000 - y)

0.04x + 0.035y = 575 (eqn 2)

0.04(15,000 - y) + 0.035y = 575

solve for y

600 - 0.04y + 0.035y = 575

600 - 0.005y = 575

-0.005y = -25

y = 5000

So the amt in acct y is $5,000

Now substitute that value into eqn 1, or simply

x = (15,000 - y) = (15,000 - 5,000) = 10,000

So the amt in acct 1 is $10,000

You can also find the amt of money earned in each acct by substituting those into eqn 2,

0.04(10,000) + 0.035(5,000) = 575

400 + 175 = 575

575 = 575

Q.E.D.

x + y = 15000

Similarly, the second account grows from y to y + 0.035y = 1.035y.

1.04x + 1.035y = 15575

You now have two equations and two unknowns. We can solve this problem!

# Comments

x + y = 15000

x + y - y = 15000 - y

x = 15000 - y

Now, substitute this expression for x in the second equation:

1.04(15000 - y) + 1.035y = 15575

Multiply the terms in parentheses by 1.04:

1.04*15000 - 1.04y + 1.035y = 15575

15600 - 1.04y + 1.035y = 15575

15600 - 0.005y = 15575

Subtract 15600 from both sides:

15600 - 0.005y - 15600 = 15575 - 15600

-0.005y = -25

Divide both sides by -0.005:

-0.005y/-0.005 = -25/-0.005

y = 5000

Go back to our simple equation relating x to y and substitute in y's value:

x = 15000 - y

x = 15000 - 5000

x = 10000

So Henry invested $10,000 in the 4% interest account and $5,000 in the 3.5% interest account.

x + y = 15000

x + y - y = 15000 - y

x = 15000 - y

Now, substitute this expression for x in the second equation:

1.04(15000 - y) + 1.035y = 15575

Multiply the terms in parentheses by 1.04:

1.04*15000 - 1.04y + 1.035y = 15575

15600 - 1.04y + 1.035y = 15575

15600 - 0.005y = 15575

Subtract 15600 from both sides:

15600 - 0.005y - 15600 = 15575 - 15600

-0.005y = -25

Divide both sides by -0.005:

-0.005y/-0.005 = -25/-0.005

y = 5000

Henry invested $10,000 in the 4% interest account and $5,000 in the 3.5% interest account.

## Comments

Henry invests $15,000 into two accounts. Let's write an equation relating x and y, the amounts invested in each of the two accounts. We know these sum to $15,000, so:

x + y = 15000

The first account earns interest at the rate of 4%. So after one year his initial investment, x, has grown to x + 0.04x = 1.04x, where 0.04x is the 4% earned.

Similarly, the second account grows from y to y + 0.035y = 1.035y.

The sum of the two accounts after one year is $15,575. We can write a second equation to describe Henry's investments after one year:

1.04x + 1.035y = 15575

You now have two equations and two unknowns. We can solve this problem!

Let's use the first equation, and solve for x. This is easily done since all we need to do is subtract y from both sides.

x + y = 15000

x + y - y = 15000 - y

x = 15000 - y

Now, substitute this expression for x in the second equation:

1.04(15000 - y) + 1.035y = 15575

Multiply the terms in parentheses by 1.04:

1.04*15000 - 1.04y + 1.035y = 15575

15600 - 1.04y + 1.035y = 15575

15600 - 0.005y = 15575

Subtract 15600 from both sides:

15600 - 0.005y - 15600 = 15575 - 15600

-0.005y = -25

Divide both sides by -0.005:

-0.005y/-0.005 = -25/-0.005

y = 5000

Go back to our simple equation relating x to y and substitute in y's value:

x = 15000 - y

x = 15000 - 5000

x = 10000

So Henry invested $10,000 in the 4% interest account and $5,000 in the 3.5% interest account.

Henry invests $15,000 into two accounts. Let's write an equation relating x and y, the amounts invested in each of the two accounts. We know these sum to $15,000, so:

x + y = 15000

The first account earns interest at the rate of 4%. So after one year his initial investment, x, has grown to x + 0.04x = 1.04x, where 0.04x is the 4% earned.

Similarly, the second account grows from y to y + 0.035y = 1.035y.

The sum of the two accounts after one year is $15,575. We can write a second equation to describe Henry's investments after one year:

1.04x + 1.035y = 15575

You now have two equations and two unknowns. We can solve this problem!

Let's use the first equation, and solve for x. This is easily done since all we need to do is subtract y from both sides.

x + y = 15000

x + y - y = 15000 - y

x = 15000 - y

Now, substitute this expression for x in the second equation:

1.04(15000 - y) + 1.035y = 15575

Multiply the terms in parentheses by 1.04:

1.04*15000 - 1.04y + 1.035y = 15575

15600 - 1.04y + 1.035y = 15575

15600 - 0.005y = 15575

Subtract 15600 from both sides:

15600 - 0.005y - 15600 = 15575 - 15600

-0.005y = -25

Divide both sides by -0.005:

-0.005y/-0.005 = -25/-0.005

y = 5000

Go back to our simple equation relating x to y and substitute in y's value:

x = 15000 - y

x = 15000 - 5000

x = 10000

So Henry invested $10,000 in the 4% interest account and $5,000 in the 3.5% interest account.

Sorry, I'm having trouble pasting my full solution in here; the web site won't accept it. Work through the problem and make sure you understand how we arrive at this answer. What you need to do is solve the first equation for x ( x = 15000 - y ) and substitute it into the second equation, and solve for y. Then use the equation I just mentioned to solve for x.

Please let me know if you have any questions.

Henry invests $15,000 into two accounts. Let's write an equation relating x and y, the amounts invested in each of the two accounts. We know these sum to $15,000, so:

x + y = 15000

The first account earns interest at the rate of 4%. So after one year his initial investment, x, has grown to x + 0.04x = 1.04x, where 0.04x is the 4% earned.

Similarly, the second account grows from y to y + 0.035y = 1.035y.

The sum of the two accounts after one year is $15,575. We can write a second equation to describe Henry's investments after one year:

1.04x + 1.035y = 15575

You now have two equations and two unknowns. We can solve this problem!

Let's use the first equation, and solve for x. This is easily done since all we need to do is subtract y from both sides.

x + y = 15000

x + y - y = 15000 - y

x = 15000 - y

Now, substitute this expression for x in the second equation:

1.04(15000 - y) + 1.035y = 15575

Multiply the terms in parentheses by 1.04:

1.04*15000 - 1.04y + 1.035y = 15575

15600 - 1.04y + 1.035y = 15575

15600 - 0.005y = 15575

Subtract 15600 from both sides:

15600 - 0.005y - 15600 = 15575 - 15600

-0.005y = -25

Divide both sides by -0.005:

-0.005y/-0.005 = -25/-0.005

y = 5000

Go back to our simple equation relating x to y and substitute in y's value:

x = 15000 - y

x = 15000 - 5000

x = 10000

So Henry invested $10,000 in the 4% interest account and $5,000 in the 3.5% interest account.

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