if the selling price of 5 pears and 4 mangoes is 41.75 while the cost of 8 pears and 5 mangoes is $2.45,what is the price of each pear and each mango?
5P+4M= 1.75
8P+5M=2.45
To find the price of each pear and each mango, we can set up a system of equations. Let's denote the price of a pear as "p" and the price of a mango as "m".
According to the given information:
5p + 4m = 41.75 (Equation 1)
8p + 5m = 2.45 (Equation 2)
We now have a system of two equations with two unknowns (p and m). We can solve this system of equations to find the values of p and m.
One way to solve this system is by using the method of substitution. Let's start by solving Equation 2 for either p or m, in terms of the other variable. We'll solve for p in terms of m:
8p + 5m = 2.45
8p = 2.45 - 5m
p = (2.45 - 5m) / 8 (Equation 3)
Now, substitute Equation 3 into Equation 1, where p is replaced by (2.45 - 5m) / 8:
5p + 4m = 41.75
5((2.45 - 5m) / 8) + 4m = 41.75
Now, we can solve the equation for m:
5(2.45 - 5m) + 32m = 166.00
12.25 - 25m + 32m = 166.00
7m = 166.00 - 12.25
7m = 153.75
m = 22.25
Now that we have the value of m, we can substitute it back into Equation 3 to find p:
p = (2.45 - 5m) / 8
p = (2.45 - 5(22.25)) / 8
p = (2.45 - 111.25) / 8
p = -108.8 / 8
p = -13.6
Since prices cannot be negative, the negative value for p should be ignored. Therefore, the price of each pear is $13.60 and the price of each mango is $22.25.