College Algebra Quiz: Systems Of Equations In Applications
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Systems Of Equations In ApplicationsQuestion 1 of 1

Two investment accounts earn different annual interest rates. Account A earns 4% annually and Account B earns 6% annually. An investor places a total of $25000 in these accounts and earns $1180 in interest after one year. If the investor wants to redistribute the funds to earn exactly $1300 in interest next year while keeping the same total investment, how much additional money needs to be moved from Account A to Account B?

$2000 needs to be moved from A to B
$3000 needs to be moved from A to B
$4000 needs to be moved from A to B
$6000 needs to be moved from A to B
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College Algebra Quiz

College Algebra Quiz: Systems Of Equations In Applications

Practice Systems Of Equations In Applications in College Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Systems Of Equations In Applications, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.

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Question 1

Two investment accounts earn different annual interest rates. Account A earns 4% annually and Account B earns 6% annually. An investor places a total of $25000 in these accounts and earns $1180 in interest after one year. If the investor wants to redistribute the funds to earn exactly $1300 in interest next year while keeping the same total investment, how much additional money needs to be moved from Account A to Account B?

  1. $2000 needs to be moved from A to B
  2. $3000 needs to be moved from A to B
  3. $4000 needs to be moved from A to B
  4. $6000 needs to be moved from A to B (correct answer)
Explanation: First, find the current distribution. Let xx = amount in Account A, yy = amount in Account B. We have x+y=25000x + y = 25000 and 0.04x+0.06y=11800.04x + 0.06y = 1180. From the first equation, y=25000−xy = 25000 - x. Substituting: 0.04x+0.06(25000−x)=11800.04x + 0.06(25000-x) = 1180, so 0.04x+1500−0.06x=11800.04x + 1500 - 0.06x = 1180, giving −0.02x=−320-0.02x = -320, so x=16000x = 16000 and y=9000y = 9000. For the new target of $1300, let $x′x' andand y′y' bethenewamounts.Weneedbe the new amounts. We need x′+y′=25000x' + y' = 25000 andand 0.04x′+0.06y′=13000.04x' + 0.06y' = 1300 .Solving:. Solving: y′=25000−x′y' = 25000 - x' andand 0.04x′+0.06(25000−x′)=13000.04x' + 0.06(25000-x') = 1300 ,so, so 0.04x′+1500−0.06x′=13000.04x' + 1500 - 0.06x' = 1300 ,giving, giving −0.02x′=−200-0.02x' = -200 ,so, so x′=10000x' = 10000 andand y′=15000y' = 15000 $. The change is from $16000 to $10000 in Account A, so $6000 moves from A to B.