suppose you bought some 32 cents stamps and some 20 cents stamps. you spent $3.92 for 16 stamps. how many of each stamp did you buy?
i got the equation--.32x + .20y = $3.92 but don't know how to solve for x and y
what class/level is this for
8th grade math
To solve the equation .32x + .20y = $3.92, where x represents the number of 32-cent stamps and y represents the number of 20-cent stamps, you can use a process called "substitution" or "elimination."
One way to approach this is to use the substitution method. Here's how you can solve it step by step:
1. Rearrange the equation so that the variables are on one side and the constant on the other side:
.32x + .20y = $3.92
Rewrite the variables in terms of cents:
32x + 20y = 392
2. Solve one equation for one variable in terms of the other variable. Let's solve for x:
32x = 392 - 20y
Divide both sides by 32:
x = (392 - 20y) / 32
3. Substitute the expression for x in the second equation:
.32 * [(392 - 20y) / 32] + .20y = $3.92
4. Simplify the equation by multiplying and simplifying the fractions:
(392 - 20y) / 100 + .20y = $3.92
5. Remove the dollar sign and multiply both sides by 100 to remove the decimal point:
(392 - 20y) + 20y = 392
6. Simplify the equation, combining like terms:
392 - 20y + 20y = 392
392 = 392
This equation is an identity, which means that it holds true for any value of y. Therefore, there are infinitely many solutions to this equation.
Since the equation has infinitely many solutions, it means that the number of 32-cent stamps and 20-cent stamps can vary, as long as the total cost is $3.92 for 16 stamps.