50000-x x is the amount of in $ ann invested in the account that pays 2.5% annual interset

- krystal

50000-x x is the amount of in $ ann invested in the account that pays 2.5% annual interset

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- anonymous

ok what are you trying to solve for?

- krystal

she invests 50,000 in two interst bearing accounts one pays 2.5 % interst and the second 3.75% at the end of one year the interest ann has earned on these is 1656.25 $ how much she invest in each of the accounts

- anonymous

ok got it!

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- anonymous

so what in an interest account, each year you earn the % of interest according to your original investment

- anonymous

so from the first account, she will earn 2.5% of 50,000

- anonymous

from the second account, she will earn 3.75% of 50,000

- anonymous

or sorry, bad first assumption

- anonymous

so we have two equations based on this information:

- anonymous

both involve amounts x and y

- anonymous

we know that .025x + .0375y = 1656.25

- anonymous

that is, the interest earned between the two accounts adds up to 1656.25, and by definition .025 of X is earned, and .0375 of y is earned in that year

- anonymous

the other thing we know is that the total amount she invests is 50,000, so x + y = 50,000

- anonymous

now since you have two variables, and two equations, you can use substitution to solve this

- anonymous

so using the second equation, we know that y = 50,000 - x

- krystal

i have to give a vebal descritpion of 50000-x

- anonymous

I'm not sure what you mean by verbal description

- anonymous

but we know that 50000 - x is the amount invested in one of the banks

- krystal

it says give a verbal description of what each of the follwoing expression represetn in the context of the problem letting x=2.5 %. 50,000 is the interest in the two accounts together

- krystal

she earned a total on the investements $1656.25

- anonymous

right. so what is the expression? 50,000 - x is the amount of money invested in the second bank, if we assume x is the amount invested in the 2.5% account

- anonymous

we know that because the total amounts are equal to 50000

- anonymous

so x+y = 50000

- anonymous

y = 50000 - x

- anonymous

and if x is the amount in the first account, 50000 - y is the amount in the 3.75% account

- anonymous

is that helping?

- krystal

i still dont get it but i think i understand ur saying if both x and y equally to 50000 than if you take away .025 away from that than it will give you the answer correct

- krystal

i need to know how to write it out

- krystal

if she has a total at the end of the year of 1656.25 it is asking how much did she invest in both accounts with one being 0.025 and one being 0.0375 annual interest

- anonymous

Since:
1. x + y = 50000
2. .025x + .0375y = 1656.25
We substitute for y in the second equation, using the first.
i.e. y = 50000 -x
Now substitute for y
.025x + .0375 (50000 - x) = 1656.25.
.025x + 1875 - .0375x = 1656.25
-.0125x = 1656.25 - 1875
-.0125x = -218.75
x = -218.75/-.0125
x = 17500

- anonymous

so looking above, she invested 17,500 in the bank with 2.5% interest rate (also known as .025 interest)

- anonymous

now that you've solved for one of the values, you can solve for the other (y) by sticking this result back into either equation

- anonymous

so x+5 = 50000

- anonymous

*x + y

- anonymous

since x = 17500, 17500 + y = 50000

- anonymous

y = 32500

- anonymous

so she invested 32500 in the second bank

- anonymous

(the one with .0375 interest)

- anonymous

now the final part is - check the answer. that is, at the end of the year, do those two values give you the correct total earned interest

- anonymous

so .025*17500 + 32500*.0375 = 437.50 + 1218.75 = 1656.25

- anonymous

so we know it's right

- anonymous

make sense?

- krystal

kinda

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