Peter Mabel sold a total of 400 Oatmeal ($1.50) and Wheat
($2) breads during the Labor Day weekend. How many of
each did Pete sell if total sales were $700?
Sold:
X Oatmeals.
(400-X) Wheats.
3x/2 + 2(400-x) = $700.
Multiply both sides by 2:
3x + 4(400-x) = 1400
3x + 1600 - 4x = 1400
-x = 1400 - 1600 = -200
X = 200.
(400-x) = 400 - 200 = 200.
NOTE: 1.50x = (1 1/2)x = (3/2)x = 3x/2.
To solve this problem, we need to set up a system of equations based on the information given.
Let's define:
Let x be the number of Oatmeal breads sold by Peter.
Let y be the number of Wheat breads sold by Peter.
According to the given information, Peter sold a total of 400 breads. So, we have our first equation:
x + y = 400
Next, we are told that the total sales were $700. Oatmeal breads sell for $1.50 each, and Wheat breads sell for $2 each. So, the second equation is:
1.50x + 2y = 700
Now, we can solve this system of equations.
One way to solve it is by substitution. We can solve the first equation for x and substitute it into the second equation:
x + y = 400
x = 400 - y
Now we can substitute x into the second equation:
1.50(400 - y) + 2y = 700
Simplifying:
600 - 1.50y + 2y = 700
0.50y = 100
y = 200
Now, substitute y = 200 back into the first equation to find x:
x + 200 = 400
x = 200
Therefore, Peter sold 200 Oatmeal breads and 200 Wheat breads during the Labor Day weekend.