Question

Last summer, Betty earned $4200 by painting houses. She invested
some of the money in a savings account that paid 3.5%/year and the
rest in a government bond that paid 4.5%/year. After one year, she has
earned $174 in interest. How much did she invest at each rate? use Elimination.

SHOW ALL STEPS

Answer 1

x*(1.035) + (4,200-x)*(1.045) = 4,374.00

1.035x + 4,389.00 -1.045x = 4,374.00

15.00  = .01x

x = 1,500  so x (or 1,500) invested at 3.5% and

(4,200 - 1,500) (or 2,700) invested at 4.5%

Answer 2

Answer: She invest $1500 in saving account and $2700 in government bond.

Step-by-step explanation:

Since we have given that

Total amount she wants to invest = $4200

Rate of interest she get in a saving account = 3.5%

Rate of interest she get in a government bond = 4.5%

Let the amount he invested in saving account be 'x'.

Let the amount he invested in government bond be 'y'

Total interest she earned = $174

According to question, it becomes,

$x+y=\ 4200--------(1)\\0.035x+0.045y=174-----(2)$

Using Elimination method, we get that

$0.035x+0.035y=147\\\\0.035x+0.045y=174\\\\-------------------------------------\\\\-0.010y=-27\\\\=\dfrac{27}{0.010}=\ 2700\\\\and\\\\x+2700=4200\\\\x=4200-2700=\ 1500$

Hence, She invest $1500 in saving account and $2700 in government bond.