Answer:
Apple: 40 cents; orange: 20 cents
Step-by-step explanation:
Use variable a to represent the cost of an apple, and variable o to represent the cost of an orange.
We are told that 5 apples and 10 oranges costs $4.
So 5a + 10o = $4.
We are also told that 3 apples and 9 oranges costs $3.
So 3a + 9o = $3.
Now, we can subtract the equations:
5a + 10o = 4
- (3a + 9o = 3)
-------------------------
2a + o = 1
Isolate variable o.
o = -2a + 1
Substitute o = -2a + 1 into an original equation. We do this so that there is only one variable left in the equation, so we can solve for the variable.
5a + 10o = 4
5a + 10(-2a + 1) = 4
Solve for a.
5a - 20a + 10 = 4
-15a + 10 = 4
-15a = -6
15a = 6
a = 6/15 = 0.40
Now we know that an apple costs 0.40 dollars, or 40 cents.
Substitute a = 0.4 into an original equation to find o.
5a + 10o = 4
5(0.4) + 10o = 4
Solve for o.
2 + 10o = 4
10o = 2
o = 2/10 = 0.20
Now we know that an orange costs 0.20 dollars, or 20 cents.
Answer:
7m^2 - 11m - 2
Step-by-step explanation:
Subtract (-3m^2 + 10m + 4) from 4m^2 - m + 2:
4m^2 - m + 2
- (-3m^2 + 10m + 4) Now distribute the negative sign:
4m^2 - m + 2
+ 3m^2 - 10m - 4
--------------------------
7m^2 - 11m - 2 is the final answer.
Answer:
You are 62 years old
Step-by-step explanation:
Let's set up an equation:
400 - 3a = 214 ( let a be your age)
Add 3a to each side:
400 = 214 + 3a
Subtract 214 from each side:
186 = 3a
Divide each side by 3:
62 = a
X = pencils, y = pens
8x + 6y = 8.50
4x + 4y = 5.....multiply by -2
----------------
8x + 6y = 8.50
-8x - 8y = -10 (result of multiplying by -2)
-----------------add
-2y = - 1.50
y = -1.50 / -2
y = 0.75 <=== pens cost 0.75
4x + 4y = 5
4x + 4(0.75) = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 0.50 <== pencils cost 0.50
Step-by-step explanation:
To find the LCM, we must check and find the value that all four denominators can divide without a remainder.
Let's take 48
Therefore: 48/8= 6
48/16= 3
48/3= 16
48/2= 24
So, we can see that clearly 48 is our LCM
Therefore; 6(3/8)+3(5/16)+16(2/3)+24(1/2)
=18/48+15/48+32/48+24/48
=(18+15+32+24)/48
=89/48