Algebra 2 help (System of equations) please?

So I understand how to solve the equation but we're doing word problems so we need to come up with the equations and then solve them. Coming up with the equations is what troubles me, I have no idea how. Some examples of the word problems are:

1) The sum of two numbers is 5. The larger number exceeds twice the smaller number by 14. Find the numbers.

2) A financial planner wants to invest $8000, some in stocks earning 15% annually and the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of $930 annually from the two investments.

3) John has 15 coins, all dimes and quarters, worth $2.25. How many dimes and how many quarters does John have?

4) A bank teller has 112 $5-bills and $10-bills for a total of $720. How many of each does the teller have?

I'm not looking for the answer, but just for someone to hopefully explain how to form equations with these types of problems. Thank you!

2 Answers

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  • 6 years ago
    Best Answer

    1) Let the larger number be x and smaller number be y

    x + y = 5

    x - 2y = 14

    SUBTRACT

    3y = -9

    y = -3 ANSWER

    x = 8 ANSWER

    2) Let the amount in stocks be $x

    0.15x + 0.06 ( 8000- x) = 930

    0.15x + 480 - 0.06x = 930

    0.09x = 450

    x = 5000

    ANSWER $ 5000 in stocks AND $ 3000 in bonds

    3) Let the quarters be x

    0.25x + 0.10( 15 -x ) = 2.25

    0.25x + 1.50 - 0.10x = 2.25

    0.15x = 0.75

    x = 5

    ANSWER 5 quarters and 10 dimes

    4) Let the no of $10 bills be x

    10x + 5 ( 112-x) = 720

    10x + 560 - 5x = 720

    5x = 160

    x = 32

    ANSWER 32 nos of $10 and 80 nos $5

  • 6 years ago

    1) x = smaller number

    y = larger number

    "The sum of two numbers is 5."

    x y = 5 <----- EQ 1

    "The larger number exceeds twice the smaller number by 14."

    y = 2x 14 <---- EQ 2

    Sub EQ 2 into EQ 1 and solve for x:

    x (2x 14) = 5

    3x = -9

    x = -3

    Use that in either equation

    y = 2*-3 14

    y = 8

    (-3,8) <--- ANS

    2) LAST ONE, YOU CAN FIGURE OUT THE REST

    "A financial planner wants to invest $8000"

    x y = 8000 <---- EQ 1

    "some in stocks earning 15% annually and the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of $930 annually from the two investments. "

    .15*x .06*y = 930

    Solve EQ 1 for either X or Y ans sub into EQ 2

    x = 8000 - y

    .15*(8000-y) .06*y = 930

    1200 - .15y .06y = 930

    -.09y = -270

    y = 3000

    Use that in either equation

    x = 8000 - 3000

    x = 5000

    (5000,3000)

    The rest are yours

    3) John has 15 coins, all dimes and quarters, worth $2.25. How many dimes and how many quarters does John have?

    X Y = 15

    .10*X .25*Y = 2.25

    4) A bank teller has 112 $5-bills and $10-bills for a total of $720. How many of each does the teller have?

    X Y = 112

    5*X 10*Y = 720

    Source(s): New Answers is glitchy... it eliminated the plus signs on my side.
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