algebra expression

Question

It cost marci 20 cents to mail a postcard and 33 cents to mail a letter shes sent either a postcard or a letter to each of 18 people and spent 4.38 total
Solve the equation to determine the number of postcards and letters that marci mailed write a sentences stating how many postcards and letters Macintosh mailed

Answer 1

Hi, Mel.

 

For this problem, we have two unknown quantities: the number of postcards mailed (x) and the number of letters mailed (y). We know that the number of postcards and letters combined is 18.

 

Also, since each postcard cost twenty cents, the cost of all the postcards is .20x (20 cents times the number of postcards). The cost of all the letters is .33y (33 cents times the number of postcards). The total cost is the sum of these two values.

 

So, we have two equations:

x + y = 18

$0.20x + $0.33y = $4.38

 

Since it is easier to solve for one variable at a time, we will use the first equation to write y in terms of x.

If x + y = 18, y = 18 - x.

 

Since y and (18 - x) are equal, we can plug in (18 - x) in the place of y in the 2nd equation.

$0.20x + $0.33y = $4.38 becomes

$0.20x + $0.33(18 - x) = $4.38

 

Now, we will solve for x (which is the number of postcards).

 

1. Distribute $0.33 to the difference in the parentheses:

$0.20x + $0.33(18) - $0.33(x) = $4.38

$0.20x + $5.94 - $0.33x

 

2. Use the associative property of addition to rearrange numbers; then, combine like terms:

$0.20x - $0.33x + $5.94 = $4.38

-$0.13x + $5.94 = $4.38

 

3. Get the variable on one side and constants (numbers without variables) on the other side:

-$0.13x + $5.94 - $5.94 = $4.38 - $5.94

-$0.13x = -$1.56

 

4. Multiply both sides by negative one to eliminate all negative signs.

(-1)(-$0.13x) = (-1)(-$1.56)

$0.13x = $1.56

 

5. Multiply both sides by 100 to eliminate decimals.

(100)($0.13x) = (100)($1.56)

$13x = $156

 

6. Divide both sides by $13 to get rid of dollar signs and to get x by itself.

($13x)/($13) = ($156)/($13)

x = 156/13 = 12

 

So, the number of postcards sold is 12. The number of letters mailed must be 18 - 12, or 6.

 

To check,

(12)($0.20) + (6)($0.33) should equal $4.38.

(12)($0.20) = $2.40; (6)($0.33) = $1.98; $1.98 + $2.40 = $4.38.