Lena bought a total of 20 postcards. She bought 6 more large poscards than small. Write a system of equations that represents the postcards Lena purchased. Solve the system by substitution. Interpret the solution.
Let x:number of small and y:big
x+y=20
y=x+6
You can solve the system now...
To represent the number of postcards Lena purchased, we can use the following system of equations:
Let's say x represents the number of small postcards that Lena bought, and y represents the number of large postcards that Lena bought.
Equation 1: x + y = 20
This equation represents the total number of postcards Lena bought, which is 20.
Equation 2: y = x + 6
This equation represents the fact that Lena bought 6 more large postcards than small postcards.
To solve the system by substitution, we can substitute the value of y from Equation 2 into Equation 1.
Substituting y in Equation 1, we get:
x + (x + 6) = 20
Simplifying the equation:
2x + 6 = 20
Subtracting 6 from both sides:
2x = 14
Dividing both sides by 2:
x = 7
Now that we have the value of x, we can substitute it back into Equation 2 to find y:
y = x + 6
y = 7 + 6
y = 13
So, the solution to the system of equations is x = 7 and y = 13, which means Lena bought 7 small postcards and 13 large postcards.
Interpretation of the solution: Lena bought 7 small postcards and 13 large postcards.