# solving equation by using substitution or elimination

1. An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.

2. A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.

3. Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?

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#### Solution Preview

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1. Cost: $x for the first artwork, $y for the 2nd artwork.

In the first exhibition:

25% on the 1st work, so the profit is 25%x = 0.25x, the total revenue is

x + 0.25x = 1.25x

10% on the 2nd work, so the profit is 10%y = 0.1y. The total revenue is

y + 0.1y = 1.1y

Total selling prices:

1.25x + 1.1y = 1520 (1)

In the second exhibition:

The revenue ...

#### Solution Summary

The solution is comprised of several algebraic application word problems. It explains how to set up the equations from the word in detail. Moreover, it shows how to solve the linear system of equations by substitution or elimination.