i dont get this algebra problem!!?

Question

Alice bought 12 apples and oranges for $2.51. If an apple costs 25 cents and an orange costs 18 cents, how many of each did she buy?

Answer 1

Let a be the number of apples
Let (12 - a) be the number of oranges

Then:
25a + 18 (12 - a) = 251 cents

Now multiply the 18 through the parentheses:
25a + 216 - 18a = 251

Subtract 216 from both sides:
25a - 18a = 35

Simplify:
7a = 35
a = 35/7
a = 5

Oranges = 12 - a
12 - 5 = 7

So Alice bought 5 apples and 7 oranges.

As a double-check:
5 apples = 5 x 0.25 = $1.25
7 apples = 7 x 0.18 = $1.26
Total = $2.51

Answer 2

Lit x be the apples Alice bought
Then the oranges she bought would be 12-x
Now an applie costs 25 cents each.
Therefor the cost of x applies would be 25x
Now the orange costs 18 cents each
Therefor the cost of (12-x) oranges would be 18(12-x)
i.e. 25x+18(12-x)= 251 cents
i.e. 25x+216-18x=251
i.e. 25xx-18x=251-216
i.e. 7x=35
i.e. x= 5
i.e. Alice bought 5 apples and 7 oranges
Cross checking
5 applies would have costed 125 cent
8 oranges would have cost 126 cents
Total 251 cents
=$2.51







































to

Answer 3

For this you can use a system of equations (I think that's what it's called...). Personally, I think this method is easier to set up than others. :)

Anyway, write what you know:

x + y = 12 --- you have 12 total of apples (x) and oranges (y)
25x + 18y = 251 --- I converted $2.51 to cents

Now multiply the first by -18 so you get one variable when you combine the two.

-18x -18y = -216
25x + 18y = 251 --- Combine the two equations, the y's cancel

7x = 35
x = 5 --- solve for x

Now that you know that x = 5, you know y must be 7, since you only have 12 apples and oranges, thus:
5 apples and 7 oranges

Answer 4

let x = apple and y = orange

So 25x + 18y = 251

you also know that x + y = 12

y = 12 - x

substitute this into the first equation

25x + 18(12 - x) = 251

25x + 216 - 18x = 251

7x = 35

x = 5, so y = 7

25*5 + 18*7 = 125 + 126 = 251

Alice bought 5 apples and 7 oranges.

Answer 5

OK its simple you begin by calling your apples A and oranges O. The problem tells you that in total Alice bought 12 between apples and oranges this means that:
A+O=12
This yields one equation
It also tells you that she spent $2.51 and that an apple costs .25 and an orange .18. This means that:
.25A+.18O=2.51
Now you have two equations with two unknown. So you can solve by saying:
A=12-O
and substituting
.25(12-O)+.18O=2.51
Manipulating the equation you get that
3-.25O+.18O=2.51
-.07O=2.51-3
-.07O=-.49
dividing on both sides you get that:
O=7
Then you substitute on the first equation and get that:
A+7=12
So,
A=12-7
A=5
Alice bought 5 apples and 7 oranges

Answer 6

If a are apples and o oranges you have: a + o = 12, and 0.25a + 0.18o = 2.51. Follows o = 7, a = 5.

Answer 7

Let A = the number of apples
Let B = the number of oranges

A + B = 12
2.51 = .25A + .18B

From the first equation we got (A + B = 12), subtract B from both sides
A = 12 - B

Using the second equation, we will substitute for A
2.51 = .25 (12 - B) + .18B
2.51 = 3 - .25B + .18B

Combine the like terms
2.51 = 3 - .07B

Subtract 3 from both sides
-.49 = .07B

Divide both sides by .07
7 = B

A + B = 12
A + 7 = 12

Subtract 7 from both sides
A = 5

5 Apples
7 Oranges

Answer 8

very easy 5 apples @25 cents = 125
7 oranges @18 cents = 126
125+126+251

Answer 9

she brought 5 apples and 7 oranges.

Answer 10

a = # of apples
b = # of oranges

a+b = 12
.25a + .18b = 2.51

a+b = 12
a = 12-b
subtitute into other equation
.25(12-b) + .18b = 2.51
3-.25b + .18b = 2.51
3 - .07b = 2.51
-.07b = -.49
b = 7

a+b = 12
b = 7
a + 7 = 12
a = 5

hope this helps!!!