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Question

Please tell me how to do it and show me the steps please :)

At the "What's up" supermarker, 3 pounds of bananas and 2 pounds of apples cost $2.85. The cost of 4 pounds of bananas and 5 pounds of apples is $5.41. What is the cost of 1 pound of bananas, and what is the cost of 1 pound of apples?

Answer 1

Let

b = bananas

a = apples

3b + 2a = 2.85- - - - - -Equation 1
4b + 5a = 5.41- - - - - -Equation 2
- - - - - - - - - - -

Multiply equation 1 by 5 and equation 2 by - 2

- - - - - -

3b + 2a = 2.85

5(3b) + 5(2a) = 5(2.85)

15b + 10a = 14.25
- - - - - - - -

4b + 5a = 5.41

- 2(4b) + (- 2)(5a) = -2(5.41)

- 8b + (- 10b) = - 10.82

- 8b - 10b = - 10.82

- - - - - - -

15b + 10a = 14.25
- 8b - 10a = - 10.82
- - - - - - - - - - - - - - -

7b = 3.43

7b / 7 = 3.43 / 7

b = 3.43 / 7

b = 0.49

Insert the b value into equation 1
- - - - - - - - - - - - - - - - - -- - - - - - --

3b + 2a = 2.85

3(0.49) + 2a = 2.85

1.47 + 2a = 2.85

1.47 + 2a - 1.47 = 2.85 - 1.47

2a = 1.38

2a / 2 = 2.38 / 2

a = 2.38 / 2

a = 0.69

Insert the a value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

3b + 2a = 2.85

3(0.49) + 2(0.69) = 2.85

1.47 + 1.38 = 2.85

2.85 = 2.85

- - - - - - - - - -

Check for equation 2

4b + 5a = 5.41

4(0.49) + 5(0.69) = 5.41

1.96 + 3.45 = 5.41

5.41 = 5.41

- - - - - - - - - -

Both equations balance

One pound of bananas cost 0.49¢

One pound of apples cost 0.69¢

- - - - - - - - - s-

Answer 2

Let b = banana and a = apple.

So, For 2 pounds of bananas and 2 pounds of apples, you get:
3b + 2a = 2.85 (equation 1)

and for 4 pounds of bananas and 5 pounds of apples you get:
4b + 5a = 5.41 (equation 2)

Now, you want either the a's or b's in both equations to be equal. I will make the a's equal.

Thus i will multiply equation 1 by 5 to give:
15b + 10a = 14.25 (equation 3)

and i will multiply equation 2 by 2 to give:
8b + 10a = 10.82 (equation 4)

Now, i will subtract equation 4 from equation 3 to give:
7b = 3.43
so, b = 3.43/7 = 0.49

Now, i will substitute b into equation 1 (you may substitute it into any of the equations):
3 x 0.49 + 2a = 2.85
1.47 + 2a = 2.85
2a = 2.85 - 1.47
2a = 1.38
a = 1.38/2 = 0.69.

Thus 1 pound of bananas costs $0.49 and 1 pound of apples costs $0.69.

Hope that is helpful!

Answer 3

a = cost of 1 pound of apples
b = cost of 1 pound of bananas

Your two equations are:

3b + 2a = 2.85
4b + 5a = 5.41

I'm going to multiply the first equation by 4 and the second by 3 (to get 12b in each) and subtract, but there are many other ways:

12b + 8a = 11.40
12b + 15a = 16.23
------------------------
-7a = -4.83

a = 0.69

Now you know that apples cost $0.69 per pound.

Either of the original equations can then be used, with the known value of a, to calculate b:

3b + 2a = 2.85
3b + 2*0.69 = 2.85
3b = 2.85 - 1.38
3b = 1.47
b = 0.49

Bananas cost $0.49 per pound.

Check with the other equation:

4b + 5a =? 5.41
4*0.49 + 5*0.69 =? 5.41
1.96 + 3.45 =? 5.41
5.41 = 5.41

Answer 4

You need to start by writing the 2 equations.
Lets say to simplify things we call bananas (x) and apples (y).
Now as you say each line, write it.
3 pounds of bananas --- 3x
2 pounds of apples --- 2y
so: 3x + 2y = 2.85

Again for the second line:
4x + 5y = 5.41

No solve one equation for either x or y and put in the second equation:
3x+2y=2.85
3x=2.85-2y
x=(2.85-2y)/3

Put into the second equation and solve for y.
4x + 5y = 5.41
4((2.85-2y)/3)+5y=5.41
(4*2.85)/3 - (4*2y)/3 +5y =5.41
3.8 - 2.67y + 5y =5.41
2.33y=1.61
y = 1.61/2.33
y = .69

Put this into the fist equation and solve for x.
3x + 2y = 2.85
3x = 2.85 - (2*.69)
3x=1.47
x = 1.47 / 3 = .49

Therefore Bananas cost x = $0.49ea.
and Apples cost y = $0.69ea.

Answer 5

- assign variables to the apples and bananas
(apples=x and bananas=y)

-create the two equations
3y+2x=2.85 and
4y+5x=5.85
-pick one of the equations and solve for a variable

3y+2x=2.85 subtract 2x

3y=2.85-2x get rid of the 3 attached to y

y=(2.85/3)-(2/30)x simplify

y=0.95-2/3x

-take the new value of y (0.95-2/3x) and plug it in place y in the other equation, the new combined equation reads=

4(0.95-2/3x)+5x=5.41

-solve

4(0.95-2/3x)+5x=5.41 distribute the 4

3.8-(8/3x)+5x=5.41 combine like terms

3.8+(7/3x)=5.41 Subtract 3.8

7/3x=1.61 multiply 1.61 by the inverse of 7/3
which is 3/7
x=0.69 this is the answer for apples, to find the answer for bananas, plug it back into either of the original equations

Answer 6

let x = price of apples
let y = price of bananas

From the information given,

i. 2x + 3y = $2.85

ii. 5x + 4y = $5.41

Multiply equation i by 5 and multiply equation ii by -2 to get

i. 10x + 15y = $14.25

ii. -10x - 8y = -$10.82

Add i and ii to get

0x + 7y = $3.43

from this you can get y = $0.49, which is the price per pound of bananas.

Plug y = $0.49 into either i or ii to get the value for x.

If you plug into i, you get:

2x + 3($0.49) = $2.85

2x = $1.38

x = $0.69, which is the price per pound of apples.

To check plug x = $0.69 and y = $0.49 into ii to see if we get the correct total price of $5.41

5($0.69) + 4($0.49) = $5.41, it checks out!

Apples = $0.69/pound and Bananas = $0.49/pound

Answer 7

x = cost per pound of bananas
y = cost per pound of apples

3x + 2y = 2.85
2y = 2.85 - 3x
y = 1.425 - 1.5x

4x + 5y = 5.41
4x + 5(1.425 - 1.5x) = 5.41
4x + 7.125 - 7.5x = 5.41
-3.5x = -1.715
x = 0.49

3x + 2y = 2.85
3(0.49) + 2y = 2.85
1.47 + 2y = 2.85
2y = 1.38
y = 0.69

1 pound of bananas costs $0.49, and 1 pound of apples costs $0.69

Answer 8

For increasing cubic binomials the final formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 9

2x+3y= 2.85
5x+4y= 5.41
(I am going to use substitution)
2x+3y=2.85
-3y -3y
2x=2.85-3y
/2 /2
x= 1.425-3/2y
5(1.425-3/2y) + 4y=5.41
7.125- 7.5y +4y = 5.410.
-3.5y =-1.715
/-3.5 /-3.5
y=0.49
2x+3(.49)=2.85
-1.47 -1.47
/2 /2
x= 0.69
bananas are .45 cents a pound and apples are 69 cents a pound

Answer 10

3b+2a=$2.85 > 12b+8a=$11.40
4b+5a=$5.41 > 12b+15a=$16.23
7a=4.83
a= $0.69
b= $0.49

I tried to align it the best i could!