I'm not sure how to solve these.
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
#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
Thanks so much! I understand the steps for #24. I see the mistake on #23.
To solve this problem using the substitution method, we can set up a system of equations based on the given information. Let's denote the amount of money invested in the first fund as "x" and the amount invested in the second fund as "y".
From the problem statement, we know that the total amount of money invested is $6000. Therefore, our first equation is:
x + y = 6000 ---- Equation (1)
Next, we can determine the interest earned from each fund. The interest earned from the first fund, at 5% annual interest, can be calculated as 0.05x. Similarly, the interest earned from the second fund, at 9% annual interest, is 0.09y. According to the problem, the total interest earned is $380. So our second equation is:
0.05x + 0.09y = 380 ---- Equation (2)
Now, we can solve this system of equations using the substitution method.
To solve for x in Equation (1), we can isolate it by subtracting y from both sides:
x = 6000 - y
Now, substitute this value of x into Equation (2):
0.05(6000 - y) + 0.09y = 380
Simplify the equation:
300 - 0.05y + 0.09y = 380
Combine like terms:
0.04y = 80
Divide both sides by 0.04:
y = 2000
Now, substitute the value of y back into Equation (1) to solve for x:
x + 2000 = 6000
x = 4000
Therefore, $4000 was invested in the first fund and $2000 was invested in the second fund.