SOLUTION: . Select the set of equations that represents the following situation: Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one yea

Question 612823: . Select the set of equations that represents the following situation: Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one year. If she had switched the amounts, she would have earned $25.84. What were the two amounts?
0.05x + 0.04y = 25.84; 0.05x + 0.04y = 21.32
5x + 4y = 21.32; 5y + 4x = 25.84
0.05x + 0.04y = 21.32; 0.05y + 0.04x = 25.84
5x + 4y = 25.84; 5x + 4y = 21.32
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your original equation is .05x + .04y = 21.32
your switched equation is .05y + .04x = 25.84
you can change your switched equation around to read .04x + .05y = 25.84 and it will mean the same thing.
you have 2 equations to solve simultaneously.
they are:
.05x + .04y = 21.32
.04x + .05y = 25.84
multiply the first equation by 4 and multiply the second equation by 5 to get:
.2x + .16y = 85.28
.2x + .25y = 129.2
subtract the first equation from he second equation to get:
.09y = 43.92
divide both sides of this equation by .09 to get:
y = 488
substitute for y in either equation to get:
x = 36
you have x = 36 and y = 488
from your first original equation, you get:
.05(36) + .04(488) = 1.8 + 19.52 = 21.32
from your second original equation, you get:
.04(36) + .05(488) = 1.44 + 24.4 = 25.84
it checks out so your answer is:
x = 36
y = 488

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