Respuesta :
Answer:
- $1800 at 6%
- $600 at 4%
Step-by-step explanation:
Let x represent the amount invested at the higher rate (6%). Then the amount invested at the lower rate is (2400-x) and the total interest earned is ...
6%·x + 4%·(2400-x) = 5.5%·2400
Dividing by % and rearranging, we have ...
x(6 -4) = 2400(5.5 -4)
x = 2400·(5.5 -4)/(6 -4) = 2400(1.5/2) = 2400·0.75
x = 1800 . . . . . . . . amount invested at 6%
2400-x = 600 . . . amount invested at 4%
Maria put $1800 in the 6% account and $600 in the 4% account.
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Comment on the solution
You will note that the proportion of the investment that went to the higher interest rate account is (5.5-4)/(6-4). This is the ratio of the mixed interest rate less the lower rate to the difference of account rates. This will be the generic solution to mixture problems, so is worthy of note for that reason.
Answer:
For 4% interest, investment $600
For 6% interest, investment $1,800
Explanation:
Maria invested $2,400 into two accounts. One account paid 4% interest and the other paid 6% interest. She earned 5.5% interest on the total investment.
It is a system of linear equations in two variables. Variables are x and y. Solve for x and y using substitution method.
In substitution method: First solve for one variable in terms of another variable and then substitute into another equation.
Further explanation:
Let $x invested in account which paying 4% interest.
Let $y invested in another account which paying 6% interest.
- Maria invested $2,400 into two accounts.
Therefore, x + y = 2400 --------------(1)
- For paying 4% interest and investment $x, Interest = 0.04x For paying 6% interest and investment $x, Interest = 0.06y
- Maria earned 5.5% interest on total investment = 0.055 × 2400
= 132
Therefore, 0.04x + 0.06y = 132 -----------(2)
Solve system of equations for x and y , using substitution method.
x + y = 2400
solve for y in terms of x and we get,
y = 2400 - x ------------ (3)
Substitute the value of y into equation (2) and we get,
0.04x + 0.06(2400-x) = 132
0.04x + 144 - 0.06x = 132
-0.02x = 132 - 144
[tex]x=\dfrac{-12}{-0.02}[/tex]
[tex]x=600[/tex]
Substitute the value of x into eq(3)
y = 2400 - 600
y = 1800
In account paying 4% interest, invest $600 and paying 6% interest invest $1,800
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Keywords:
System of equation, Two variable equations, solve for x and y, substitution method, elimination method, cross multiplication method.
