four apples and 2 ponkans cost 53.two apples and four ponkans cost 75.how much will half a dozen apples and half a dozen ponkans cost?
Let A = cost of one apple
Let P = cost of one ponkan
According to the first statement,
4A + 2P = 53
According to the second statement,
2A + 4P = 75
Now we're looking for 6A + 6P (because half a dozen is equal to six). Notice that if we add the equations, we'll get 6A + 6P:
4A + 2P = 53
2A + 4P = 75
------------------
6A + 6P = 128
Thus the cost is 128.
Hope this helps :)
thanks... God bless Jai!!!
To find the cost of half a dozen apples and half a dozen ponkans, we first need to determine the cost of one apple and one ponkan.
Let's assign variables:
Let A be the cost of one apple, and
Let P be the cost of one ponkan.
From the given information, we have two equations:
1. Four apples and 2 ponkans cost 53:
4A + 2P = 53 --(equation 1)
2. Two apples and four ponkans cost 75:
2A + 4P = 75 --(equation 2)
We can solve this system of equations by using the method of substitution:
From equation 1, we can rewrite it to solve for A:
4A = 53 - 2P --> A = (53 - 2P)/4
Now we substitute the value of A into equation 2:
2((53 - 2P)/4) + 4P = 75
Multiplying both sides by 4 to remove the fraction:
2(53 - 2P) + 16P = 300
106 - 4P + 16P = 300
12P = 300 - 106
12P = 194
P = 194/12
P ≈ 16.17
Now we can find A by substituting the value of P into equation 1:
4A + 2(16.17) = 53
4A + 32.34 = 53
4A = 53 - 32.34
4A = 20.66
A = 20.66/4
A ≈ 5.16
Therefore, the cost of one apple (A) is approximately $5.16, and the cost of one ponkan (P) is approximately $16.17.
Now, let's calculate the cost of half a dozen apples (6 apples) and half a dozen ponkans (6 ponkans):
Cost of half a dozen apples = 6 * A
Cost of half a dozen ponkans = 6 * P
Substituting the values we found:
Cost of half a dozen apples = 6 * 5.16 ≈ $30.96
Cost of half a dozen ponkans = 6 * 16.17 ≈ $97.02
Therefore, half a dozen apples and half a dozen ponkans would cost approximately $30.96 + $97.02 = $128.98.