3 apples plus 2 pears cost .78 but 2 apples and 3 pears cost .82. What is the cost of 1 apple and 1 pear?
3a+2p=.78
2a+3p=.82
#1 x 3 : 9a+6p=2.34
#2 x 2 : 4a+6p=1.64
subtract them ...
5a = .70
a=.14
in #1
3(.14) + 2p = .78
p = .18
so 1 apple and 1 pear = .....
A box full of exercise books weigh 12kg.if one exercise book weigh 10.2g.find the approximate number of exercise books in the box
Gimme the answer
Mugmogblug
Well, it seems like the fruits are having a pricing circus! Let's solve this fruity riddle.
Let's call the cost of an apple "a" and the cost of a pear "p".
From the first statement, we can set up the equation:
3a + 2p = 0.78
And from the second statement:
2a + 3p = 0.82
Now, let's put on our math clown noses and solve this!
Multiply the first equation by 2, and the second equation by 3 to eliminate a:
6a + 4p = 1.56
6a + 9p = 2.46
Subtract the first equation from the second equation:
6a + 9p - (6a + 4p) = 2.46 - 1.56
Simplify that equation:
5p = 0.9
Divide each side by 5:
p = 0.18
Now, substitute the value of p back into either of the original equations, let's use the first one:
3a + 2(0.18) = 0.78
Simplify:
3a + 0.36 = 0.78
Subtract 0.36 from both sides:
3a = 0.42
Divide both sides by 3:
a = 0.14
So, the cost of 1 apple and 1 pear is $0.14 + $0.18, which equals $0.32.
Looks like the clown cars parked right next to the fruit stand, and now we have the answer!
To solve this problem, we can set up a system of equations to represent the given information.
Let's represent the cost of 1 apple as "a" and the cost of 1 pear as "p".
From the first piece of information, we know that 3 apples plus 2 pears cost $0.78, so we can write the equation:
3a + 2p = 0.78 ----(1)
From the second piece of information, we know that 2 apples and 3 pears cost $0.82, so we can write the equation:
2a + 3p = 0.82 ----(2)
Now, we can solve this system of equations to find the values of "a" and "p".
To do so, we can use a method called substitution:
1. Solve equation (1) for one variable (either "a" or "p"). Let's solve it for "a" by isolating "a" on one side:
3a + 2p = 0.78
3a = 0.78 - 2p
a = (0.78 - 2p) / 3
2. Substitute this expression for "a" in equation (2):
2((0.78 - 2p) / 3) + 3p = 0.82
Simplify the equation:
(1.56 - 4p) / 3 + 3p = 0.82
3. Multiply both sides of the equation by 3 to remove the fraction:
1.56 - 4p + 9p = 2.46
4. Combine like terms:
5p + 1.56 = 2.46
5. Subtract 1.56 from both sides of the equation:
5p = 2.46 - 1.56
5p = 0.9
6. Divide both sides of the equation by 5 to solve for "p":
p = 0.9 / 5
p = 0.18
Now, we have the value of "p" which represents the cost of 1 pear.
To find the cost of 1 apple, we can substitute this value of "p" back into equation (1):
3a + 2(0.18) = 0.78
Simplifying the equation:
3a + 0.36 = 0.78
Subtract 0.36 from both sides of the equation:
3a = 0.78 - 0.36
3a = 0.42
Divide both sides of the equation by 3 to solve for "a":
a = 0.42 / 3
a = 0.14
Therefore, the cost of 1 apple and 1 pear is $0.14 + $0.18 = $0.32.