Word Sentences for Algebra

Question

Two investments totaling $16,000 produce an annual income of $1,140. One investment yields 6% a year, while the other yields 8% per year. How much is invested at 8%?

Answer 1

Step 1: Define your variables

Total Investments = $16,000 = X₁ + X₂

Investment 1 Yield Rate - 6% (0.06) = r₁

Investment 2 Yield Rate - 8% (0.08) = r₂

Yearly income from investments = $1,140 = X₁*r₁ + X₂*r₂

Step 2: Arrange variables for solving

Two variables, two equations -> Solve for one (I will pick X₁)

Equation 1: $16,000 = X₁ + X₂ -> X₁ = 16000 - X₂

Equation 2: $1,140 = X₁*r₁ + X₂*r₂

Step 3: Solve for Variable (X₁)

1140 = (16000 - X₂)*(0.06)+X₂*(0.08)

1140 = 960 + 0.02*X₂

180 = 0.02*X₂

X₂ = 9000

X₁ = 16000 - 9000 = 7000

Step 4: Present Solution

There is $7,000 at the r₁ = 6% rate and $9,000 at the r₂ = 8% rate.

Answer 2

Let "x" represent the first investment and let "y" represent the second investment.

We are told that the two investment total (or add up to) $16,000 so we can say x + y = 16000.

We are also told that the 1st investment yields 6% (or 0.06 in decimal form) which means that (0.06)multiplied by the first investment will tell us how much money the 1st investment earned that year. And the same with the 2nd investment, it would produce (0.08)y during the year.

We are also told that the total earned is $1,140 which means 0.06x + 0.08y = 1140.

So we have 2 equations in 2 unknowns:

x + y = 16000

0.06x + 0.08y = 1140

There are several ways of solving these. A fairly easy way is to use substitution. The first equation could also be written as x = 16000 - y

Since "x" and "16000 - y" are equal, we can substitute "16000 - y" for "x" in the 2nd equation:

0.06(16000 - y) + 0.08y = 1140

Can you solve this for "y"?

Once you solve this for "y" you can plug the value into x = 16000 - y to find out what the other investment is.

Answer 3

1140/1600 = 7 1/8 % = 0.07125

= average income percentage

It's a little closer to 8 than to 6, so slightly more invested at 8%, a little over half of $16K or maybe $9,000 or so

.08x + .06(16-x) = 1.14

.08x-.06x = 1.14 - 0.96 = .18

x = .18/.02 = $9,000 invested at 8%

.08(9) + .06(7) = .72+.42 = 1.14 thousand dollar total invested