Lisa went to the store and bought 100 pounds of fruit for $100.00. The peaches were $10.00 a pound, the melons were $3.50 per pound, and the apples were $.50 per pound. How many pounds of each did she buy
amount of peaches --- x lbs
amount of melons ---- y lbs
amount of apples ----- 100 - x - y lbs
(assume both x and y are whole numbers)
10x + 3.5y + .5(100-x-y) = 100
double every term
20x + 7y + 100 - x - y = 200
19x + 6y = 100
x = (100 - 6y)/19 , clearly 0 < y < 6
by trials, y = 4, then x = 4
So he bought 4 lbs of peaches,
4 lbs of melons, and
92 lbs of apples.
check:
10(4) + 3.5(4) + .5(92)
= 40 + 14 + 46
= 100
To determine how many pounds of each fruit Lisa bought, we can use a system of equations. Let's denote the number of pounds of peaches, melons, and apples she bought as p, m, and a respectively.
From the given information, we know:
1) p + m + a = 100 (the total number of pounds of fruit is 100)
2) 10p + 3.50m + 0.50a = 100 (the total cost of fruit is $100)
Now we can solve this system of equations to find the values of p, m, and a.
One way to solve this is by substitution. Rearrange equation 1 to solve for a: a = 100 - p - m. Then substitute this value of a into equation 2:
10p + 3.50m + 0.50(100-p-m) = 100
Simplify the equation:
10p + 3.50m + 50 - 0.50p - 0.50m = 100
9.50p + 3m + 50 = 100
Subtract 50 from both sides:
9.50p + 3m = 50
Now we have two equations:
p + m = 100
9.50p + 3m = 50
We can solve this system of equations using various methods, such as substitution or elimination. Here, we will use the substitution method:
From equation 1, we have p = 100 - m.
Substitute this into equation 2:
9.50(100 - m) + 3m = 50
950 - 9.50m + 3m = 50
950 - 6.50m = 50
Subtract 950 from both sides:
-6.50m = -900
Divide both sides by -6.50 (or multiply by -1 to simplify):
m = 138.46
Since we cannot have a fraction of a pound, we can round down to the nearest whole number:
m = 138 pounds.
Now substitute the value of m back into equation 1 to find p:
p + 138 = 100
p = 100 - 138
p = -38
Similarly, we cannot have negative pounds, so it implies an error in the given information or calculations.
Hence, it seems the given information or calculations may be incorrect, as it leads to a contradiction.