I'm not sure how to solve these.

Question

Solve using any method (substitution or elimination)
23. The sum of two numbers is 27. The larger number is three more than the smaller number. What are the two numbers?
Ans:
l = large; s = small
l + s =27 and l = 3S

3s + s =27
4s =27
4s/4 = 27/4
s = 6.75

solve for l:
l = 3(6.75)
l = 20.25

large number = 20.25 and small number = 6.75

24. You have $6000 to invest in two stock funds. The first fund pays 5% annual interest and the second pays 9% annual interest. If after a year you have made $380 in interest, how much money did you invest in each account?

Ans:
x = first fund, y = second fund

5x + 9y = 6000
?not sure what 2nd equation should be

Answer 1

#23
The larger number is three more than the smaller
---- l = s + 3
you had "the larger is 3 times the smaller"

l - s = 3
l + s = 27
add them
2l = 30
l = 15
and 15+s= 27
s = 12

24.
5% ---> .05, so
.05x + .09y = 380
multiply by 100
5x + 9y = 38000 **
first equation should have been
x + y = 6000 *

multiply * by 5,
5x + 5y = 30,000
5x + 9y = 38,000
subtract them:
4y = 8,000
y = 2000
then x = 4000

Answer 2

Thanks so much! I understand the steps for #24. I see the mistake on #23.