Solving using 2 equations in two variable: Jason bought a total of 7 postcards for 1.80. If small cost 20 cents and the large ones cost 30 cents, how many postcards of each size did he buy?
The answer is 3 small and 4 large. I just do not know how to get there...L cannot equal 9 there are only 7 cards.
Thank you please help me know how to solve.
Eq1: S + L = 7.
Eq2: 0.2S + 0.3L = 1.8.
Multiply both sides of Eq1 by -0.2 and add the Eqs:
-0.2S - 0.2L = -1.4
0.2S + 0.3L = 1.8
Sum: 0.1L = 0.4
L = 4.
In Eq1, replace L with 4 and solve for S.
To solve this problem using two equations in two variables, let's define the variables.
Let's say x represents the number of small postcards and y represents the number of large postcards.
According to the problem, Jason bought a total of 7 postcards, so we have the equation:
x + y = 7 (Equation 1)
The cost of a small postcard is 20 cents, and the cost of a large postcard is 30 cents. The total cost of all the postcards that Jason bought is $1.80, which can be written as 180 cents.
The cost equation can be expressed as:
20x + 30y = 180 (Equation 2)
Now, we have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the substitution method:
From Equation 1, we have: x = 7 - y
Now, substitute this into Equation 2:
20(7 - y) + 30y = 180
Simplify that equation:
140 - 20y + 30y = 180
10y = 40
y = 4
So, we've found that the number of large postcards (y) is 4.
Substitute y = 4 back into Equation 1 to find x:
x + 4 = 7
x = 7 - 4
x = 3
Therefore, Jason bought 3 small postcards (x) and 4 large postcards (y).
S + L = 7
.2 S + .3 L = 1.8 ... S + 1.5 L = 9