How much of the $19,000 did the bank loan out at 7%?

Question

A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2500, how much was loaned at 7%?

Answer 1

.17x + .07(19000-x) = 25000

.10x = 25000 - .07(190+00 = 25000 - 13300 = 11700

x = $11,700 at 17%

y = $7,300 at 7%

.17(11700) + .07(7300) = 2400 It works

or an alternative solution method:

2500/19000 = 25/190 = 5/38= 0.13157894.... = 13 5/38 %

= average return % rate, for 17 and 7% (not (17+7)/2=12%)

17 - 13 5/38= 3 33/38

13 5/38 -7 = 6 5/38

(6 5/38)/(3 33/38)

= (233/38)/(147/38)

= (233/38)(38/147)

= 233/147=x/y

233/147 = x/y where x = amount of 17% y = amount of 7%= 19000-x= 19K -x where K=$1000

x/(19K-x) = 233/147 cross multiply to get

147x = 233(19K) -233x

380x = 233(19K) divide by 190

2x = .1K(233)=100(233) divide by 2

x = 100(233)/2=50(233) = $11,650 at 17%

y = 19000-11650 = $7,350 at 7% slight mistake somewhere but very close with 2nd method

go with 1st solution, likely mistake in 2nd