Can someone help me with some algebra 2 word problems?

Question

Can someone also show and explain step-by-step how they got the answer? I would really appreciate it. These problems are from a lesson that's titled System of Linear Equations.

1)Ten pounds of mixed birdseed sell for $6.97 per pound. The mixture is obtained from two kinds of birdseed, with one variety priced at $5.65 per pound and the other at $8.95 per pound. How many pounds of each variety of birdseed are used in the mixture.?

2)How many tons of hay at $125 per ton must be purchased with hay at $75 per ton to have 100 tons of hay with a value of $90 per ton?

3)A total of $20,000 is invested in two bonds that pay 8% and 9.5% simple interest. The annual interest is $1675. How much is invested at each fund?

4)You must cut a rope that is 160 inches long into two pieces so that one piece is four times as long as the other. Find the length of each piece.

Answer 1

1) (5.65)(x)+(8.95)(10-x)=(10)(6.97)

     5.65x+89.5-8.95x=69.7

    -3.3x+89.5=69.7

    -3.3x=69.7-89.5

    -3.3x=-19.8

     3.3x=19.8

      33x=198

         x=198/33

         x=6 pounds

         10-x=4 pounds

 

2) (125)(x)+(75)(100-x)=(100)(90)

    125x+7500-75x=9000

    50x+7500=9000

    50x=9000-7500

    50x=1500

        x=1500/50

        x=30

        100-x=70

 

3) (8%)(x)+(9.5%)(20,000-x)=$1675

     0.08x+1900-0.095x=1675

     -0.015x=1675-1900

     -0.015x=-225

           15x=225,000

               x=225,000/15

               x=$15,000 and $5000

 

4) x and 4x are the pieces

    x+4x=160

        5x=160

          x=160/5

          x=32 inches and 4x=128 inches