Can someone please help with this?
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¢ stamps did Allen buy?
A) 15
B) 16
C) 17
D) 18
Set up a system of equations to model this situation. (Note that a system of equations is TWO different equations.)
Let x be the number of 37-cent stamps, and let y be the number of 20-cent stamps.
What two equations did you get?
x+y=7.06
That's only one equation.
Anyway, the number of stamps that he buys is 20.
The other equation will deal with the stamp prices.
What do you get?
37x+20y=7.06
That's close. The stamps are in CENTS, though.
.37x + .20y = 7.06
That is one equation. The other equation deals with how many stamps he bought. What is it?
x+y=20
and
37x + .20y = 7.06
Good. Our two equations are:
.37x + .20y = 7.06
x + y = 20
We're trying to find the number of 37-cent stamps (x). We can solve this system of equations by substitution. Solve the second equation for y, and then plug that into the first equation.
We now only have x's in the equation, so solve it as you would any other equation.
Would the answer be D - 18 .37 stamps?
Yup. Nice job.
To solve this problem, we can use a system of equations.
Let's assume Allen bought x stamps in the 37¢ denomination and y stamps in the 20¢ denomination.
From the given information, we know that the total cost of the stamps is $7.06. Therefore, we can write the equation:
37x + 20y = 706 ... (1)
We also know that Allen bought a total of 20 stamps. So the second equation can be written as:
x + y = 20 ... (2)
Now we will solve this system of equations to find the values of x and y.
First, let's multiply equation (2) by 20 to eliminate fractions:
20x + 20y = 400 ... (3)
Now, let's subtract equation (3) from equation (1) to eliminate y:
37x + 20y - (20x + 20y) = 706 - 400
17x = 306
x = 306 / 17
x ≈ 18
So, Allen bought approximately 18 stamps in the 37¢ denomination.
Therefore, the answer is D) 18.