Answer:
0,7
Step-by-step explanation:
The answer can be readily calculated using a single variable, x:
Let x = the amount being invested at an annual rate of 10%
Let (8000 - x) = the amount being invested at an annual rate of 12%
The problem is then stated as:
(x * 0.10) + ((8000 - x) * 0.12) = 900
0.10(x) + ((8000 * 0.12) - 0.12(x)) = 900
0.10(x) + 960 - 0.12(x) = 900
0.10(x) - 0.12(x) = 900 - 960
-0.02(x) = -60
-0.02(x) * -100/2 = -60 * -100/2
x = 6000 / 2
x = 3000
Thus, $3,000 is invested at 10% = $300 annually; and $8,000 - $3,000 = $5,000 invested at 12% = $600 annually, which sum to $900 annual investment.
Of course.
You can only say for sure that 1/4 of a whole thing is less than 1/3 of a whole thing
if the whole things are equal size.
If Marty's pizza was 1/3 bigger than Luis' pizza, then they both ate the same amount.
If Marty's was MORE than 1/3 bigger than Luis', then Marty ate more pizza.
You would first have to find common denominators for the fractions. In this case it would be 10. So your new equation would be 3 5/10 - 2 4/10. Once you do this you can then subtract and solve getting the answer of 1 1/10
1/2r -3= 3 (4-3/2r) is to be solved for r.
I'll begin by making the assumptions that by 1/2r you actually meant (1/2)r and that by 3/2r you actually meant (3/2)r. When in doubt, please use parentheses to make your meaning clear.
Thus, 1/2r -3= 3 (4-3/2r) becomes (1/2)r -3= 3 (4-(3/2)r ) .
Simplify this by multiplying all 3 terms by 2. Doing this will eliminate the fractions:
r -6 = 3 (4*2-(3)r ) or r - 6 = 24 - 9r
Now expand the right side, using the distributive property of
r - 3 = 24 - 9r
Regrouping so as to combine like terms:
10r = 30
Solving for r: r = 30/10 = 3
The value of r that satisfies this equation is 3
