What do you do?

Question

Allen bought 20 stamps at the post office in 37¢ and 20¢ denominations. If the total cost of the stamps was $7.06, how many 37¢ did Allen buy?

Answer 1

Substitution Method

x + y = 20- - - - - - - - - - - -- Equation 1
0.37x + 0.2y = 7.06- - - - - Equation 2
- - - - - - - - - - - - - - -

x + y = 20

x + y - x = - x + 20

y = - x + 20

Substitute the y value into equation 2
- - - - - - - - - - - -

0.37x + 0.2y = 7.06

0.37x + 2(- x + 20) = 7.06

0.37x + (- 0.2x + 4) = 7.06

0.37x - 0.2x + 4 = 7.06

0.17x + 4 = 7.06

0.17x + 4 - 4 = 7.06 - 4

0.17x = 3.06

0.17x / 0.17 = 3.06 / 0.17

x = 3.06 / 0.17

x = 18. . . .Number of 0.37¢ stamps

Insert the x value into equation 1

- - - - - - - - - - -

x + y = 20

18 + y = 20

18 + y - 18 = 20 - 18

y = 2. . . . .Number of 0.2¢ stamps

Insert the y value into equation 1

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

Check for equation 1

x + y = 20

18 + 2 = 20

20 = 20

- - - - - - - -

Check for equation 2

0.37x + 0.2y = 7.06

0.37(18) + 0.2(2) = 7.06

6.66 + 0.4 = 7.06

7.06 = 7.06

- - - - - - - - - - -

Both equations balance

0.37¢stamps = 18

0.2¢ stamps = 2

- - - - - - - -s-

Answer 2

Allen bought 20 stamps at the post office in 37¢ and 20¢ denominations. If the total cost of the stamps was $7.06, how many 37¢ did Allen buy?

Let’s say he bought t stamps at 37¢. If you buy t stamps at 37¢, you must pay 37t cents for them. 3

If he bought a total of 20 stamps, and t of them cost 37¢ each, then he bought 20-t stamps at 20¢, and paid 20(20-t) cents for them.

You said the total he paid was $7.06, or 706¢. Tat means that 37t + 20(20-t) = 706

First distributing the multiplication by 20 over (20-t),, you have 37t + 400 - 20t = 706 because 10x20=400.

Combining terms we get
17t = 306, and multiplying both sides by 1/17, you
t = 18

That means he purchased 18 stamps at 37¢.

Just to check, if he purchased 18 at 37¢ and if the total number purchased was 20, then he purchased 2 at 20¢. 18x37 + 2x20 = 666 + 40 = 706. It checks.

Answer 3

Let x be the number of 37¢ stamps Allen bought.

(20-x)(20)+x(37) = 706

Solve for x,
x = 18

Answer 4

You're going to have two equations.
From the info. you can set it up like this:
x will be the number of .37 stamps and y the number of .20 stamps
.37x+.20y=7.06
x+y=20

Now you have a system of equations. Set the bottom one equal to y

y=20-x
Now put 20-x in for y in the first equation.
.37x+.2(20-x)=7.06
.37x+4-.2x=7.06
.17x+4=7.06
.17x=3.06
x=18
So he bought 18 stamps for $.37. Now put 18 in for x in either equation and you can figure out y.
Let's do the second.
18+y=20
y=2
So he bought 2 stamps for $.20.

Answer 5

Let x be the number of stamps costing 37 cents he bought. This means he bought (20-x) stamps that costed 20 cents.

Thus you get the equation

0.37*x + 0.2*(20-x)=7.06

Just solve the equation for x.

Answer 6

A + B = 20 B = 20 - A

37 * A + 20 * B = 706

37 * A + 20 * (20 - A) = 706

37 * A + 400 - 20 * A = 706

17 * A = 306

A = 18

B = 2