Algebraic question?

Question

4 oranges and 5 apples cost $3.56
If 3 oranges and 4 apples cost $2.76
find the cost of 1 apple and 1 orange
use algebraic equation

I do not understand this

Can someone also include the algebriac equation like this..

A= 3.56-4o O= 2.76-4a
---------- -----------
5 3

I am not sure if this is correct but this is how I belive it should look?
Thank you

Can someone also include the algebriac equation like this..

A= 3.56-4o O= 2.76-4a
---------- -----------
5 3

I am not sure if this is correct but this is how I belive it should look?
Thank you

Can someone also include the algebriac equation like this..

A= 3.56-4o
----------
5

O= 2.76-4a
----------
3

I am not sure if this is correct but this is how I belive it should look?
Thank you

Answer 1

cost of 4 oranges+5 apples=$3.56
cost of 3 oranges+4 apples=$2.76
(subtrcting) cist of 1 orange+1 apple=$0.80

Answer 2

1: 4o + 5a = 356 (work with pennies: no decimals to deal with)
2: 3o + 4a = 276

Lets multiply the top equation by 3 and the bottom by 4

1: 12o + 15a = 1068
2: 12o + 16a = 1104

Just to make it easier, I'm going to replace the order of the equations.

2: 12o + 16a = 1104
1: 12o + 15a = 1068

Now, subtract the second equation from the first and you get

. . 0 . . . . + a . . = 36

So a = 36

Going back to the first equation

4o + 5a = 356
4o + 5 * 36 = 356
4o + 180 = 356
4o = 176
o = 44

so o + a = 44 + 36 = 80

Answer 3

4o + 5a = 356 cents (it is easier that way)

3o + 4a = 276

So 1o + 1a = 80 (equation 3)

Let us multiply the first equation by 3 and the second equation by 4.

We get

12o + 15a = 1068
12o + 16a = 1104

So we get 1 a = 1104 - 1068 = 36 cents

and substituting that in equation 3,

1o + 36 = 80

orange = 80 - 36 = 44 cents

So an orange costs 44 cents and an apple costs 36 cents.

Answer 4

You need to find the value of oranges and apples, So lets assign a value to each. How about:

Let price of oranges = X
Let price of Apples = Y

So lets use what we already have:

4X + 5Y = 3.56
3X+ 4Y = 2.76

At this point you could pick either equation. Lets do the bottom one. Lets get X alone:
3X+4Y = 2.76
3X = 2.76 - 4Y
X= (2.76 - 4Y)/3

Cool. Now we know X in terms of Y. Lets go to the first equation now.
4X + 5Y = 3.56 We can substitute X for its value in terms of Y.
4((2.76-4Y)/3) +5Y = 3.56 Then we can distribute the four through.
(11.04 - 16Y)/3 + 5Y = 3.56 Multiply both sides by 3 to get rid of that messy fraction.
11.04 - 16Y + 15Y = 10.68 Now just get Y alone.
-16Y +15Y = -.36
-Y = -.36
Y = .36

Cool, so now we have the dollar value of Y. Now it wil be easy to get the dollar value of X.

4X + 5Y = 3.56
4X + 5(.36) = 3.56
4X + 1.8 = 3.56
4X = 1.76
X = .44

There you have it, oranges cost 44 cents, apples cost 36.

Answer 5

First we need to change the information into equations.

4 oranges + 5 apples = $3.56 (Equation 1)
3 oranges + 4 apples = $2.76 (Equation 2)

Equation 1 - Equation 2,
1 orange + 1 apple = $0.80
3 oranges + 3 apples = $2.40 (Equation 3)

Equation 2 - Equation 3,
1 apple = $0.36

Therefore,
1 orange + $0.36 = $0.80
1 orange = $0.44

Answer 6

So, you would find equation 1 and equation 2:

x=orange
y=apple
Equation 1: 4x+5y=3.56
Equation 2: 3x+4y=2.76

Then you could solve through graphing, elimination, or substitution.

I did used elimination:
x=orange
y=apple
-3(4x+5y=3.56)
4(3x+4y=2.76)

-12x-15y=-10.68
12x+16y=11.04
(x cancels out)
y=0.36
(substitute 0.36 in for y in on of the previous equations)
4x+5(0.36)=3.56
4x+1.8=3.56
(subtract both sides by 1.8)
4x=1.76
(divide both sides by 4)
x=0.44

So, x=0.44 and y=0.36. So, there an orange costs $0.44 and an apple costs $0.36.

Answer 7

orange = x apple =y

4x+5y=3.56
3x + 4y = 2.76

isolate one varible and substitute:
3x = 2.76-4y
x = 0.92-4/3y
substitute:
4(0.92-4/3y) +5y = 3.56
3.68 - 16/3y + 5y = 3.56
-16/3y+5y = 3.56-3.68
-16/3Y + 5y = -.12
-1/3Y = -0.12
y = 0.36

Answer 8

4O + 5A = 3.56 -------> (1)
3O + 4A = 2.76 -------> (2)

(1) - (2)
1O + 1A = 0.8
1A = 0.8 - 1O ----> (3)

(1) + (2)
7O + 9A = 6.32
9A = 6.32 - 7O ------ (4)

(3) in (4)
9 [0.8 - 1O] = 6.32 - 7O
1O = 0.44

Subs. 1O = 0.44 in (3), you'll get 1 apple = 0.36