Samuel bought three cups and four spoons for Kshs 324. Daniel bought five cups and Mary bought two sppons of the same type as those bought by Samuel. Daniel paid Kshs 228 more than Mary. Find the price of each cup and spoon.
1cup=60
1spoon=36
Let's assume the price of each cup is 'c' and the price of each spoon is 's'.
Based on the given information, we can set up two equations:
3c + 4s = 324 ---(1) (Samuel's purchase)
5c + 2s + 228 = 2s ---(2) (Daniel's and Mary's purchases)
We can simplify equation (2) by eliminating 's':
5c + 2s + 228 - 2s = 0
5c + 228 = 0
5c = -228
c = -228/5
c = -45.6
Since the price cannot be negative, we discard the negative value of 'c'.
Hence, the price of each cup is Kshs 45.6.
Now, substituting the value of 'c' in equation (1) to solve for 's':
3(45.6) + 4s = 324
136.8 + 4s = 324
4s = 324 - 136.8
4s = 187.2
s = 187.2/4
s = 46.8
Hence, the price of each spoon is Kshs 46.8.
Therefore, the price of each cup is Kshs 45.6 and the price of each spoon is Kshs 46.8.
Let's assume the price of a cup is "x" and the price of a spoon is "y".
According to the given information, Samuel bought three cups and four spoons for Kshs 324. So the total cost of cups and spoons for Samuel is:
3x + 4y = 324 ----- (Equation 1)
Daniel bought five cups, so the cost of cups for Daniel would be 5x. Mary bought two spoons, so the cost of spoons for Mary would be 2y.
According to the given information, Daniel paid Kshs 228 more than Mary. Therefore, the equation can be expressed as:
5x = 2y + 228 ----- (Equation 2)
Now we can solve these two equations simultaneously to find the values of x and y.
Multiply Equation 2 by 2 to eliminate the "2y" term:
10x = 4y + 456 ----- (Equation 3)
Now we can subtract Equation 1 from Equation 3 to eliminate the "4y" term:
10x - 3x = 4y + 456 - 3x - 324
7x = 132
Divide both sides of the equation by 7:
x = 132 / 7
x = 18
Now substitute the value of x back into Equation 1 to find y:
3(18) + 4y = 324
54 + 4y = 324
4y = 324 - 54
4y = 270
Divide both sides of the equation by 4:
y = 270 / 4
y = 67.5
Therefore, the price of each cup is Kshs 18 and the price of each spoon is Kshs 67.5.
price of cup ---- x
price of spoon --- y
Samuel:
3x+4y=324
Daniel paid 5x for his cups
Mary paid 2y for her spoons
5x - 2y = 228
double this last equation
10x-4y=456 , add to the first
3x+4y=324
13x = 780
x = 60
back in 1st:
3(60) +4y = 324
I will let you finish it , and state the conclusion