Mr Lok has a total of 320 cups and jars at first. After 1/3 of the cups and 1/2 of the jars were sold, there were as 4/5 as many cups as jars left. What was the total number of cups and jars sold?
c + j = 320 or j = 320 - c
2/3 c = (4/5)(1/2 j) = 2/5 j
10 c = 6 j = 6 (320-c)
10 c = 1920- 6 c
16 c = 1920
c = 120
then j = 200
120 / 3 = 40 cups sold
100 jars sold
140 objects sold
That last part we can ignore, we can just use the fractions in the first part of the information.
1/3 of 320 cups is 320 x 1/3 = 320/3 = 106 or 107 cups
1/2 of 320 jars is 320 x 1/2 = 320/2 = 160 jars
Hope this helps!
"........ total of 320 cups and jars ...."
Is indeed a bit ambiguous.
Anonymous is correct.
To solve this problem, we'll set up an equation based on the given information.
Let's assume the number of cups Mr. Lok had initially is C, and the number of jars he had initially is J.
According to the problem, Mr. Lok had a total of 320 cups and jars at first, so we can set up the following equation:
C + J = 320 ...........(1)
Now, it is mentioned that after 1/3 of the cups and 1/2 of the jars were sold, there were 4/5 as many cups as jars left. Let's calculate the remaining number of cups and jars based on this information.
After selling 1/3 of the cups, the number of cups left will be (2/3)C.
After selling 1/2 of the jars, the number of jars left will be (1/2)J.
According to the problem, the remaining cups (2/3)C is 4/5 times the remaining jars (1/2)J. We can set up another equation based on this information:
(2/3)C = (4/5)(1/2)J
Simplifying the equation, we get:
(2/3)C = (2/5)J ...........(2)
Now we have a system of two equations (equations 1 and 2) with two variables (C and J). We can solve this system to find the values of C and J.
Let's multiply equation 1 by 5, and equation 2 by 3 to eliminate the fractions:
5C + 5J = 1600 ...........(3)
6C = 6J ...........(4)
Now we can substitute equation 4 into equation 3:
5(6J) + 5J = 1600
30J + 5J = 1600
35J = 1600
J = 1600/35
J ≈ 45.71
Since the number of jars must be a whole number, we can assume that Mr. Lok initially had 46 jars.
Substituting J = 46 into equation 4, we can find the value of C:
6C = 6(46)
C = 276
Therefore, Mr. Lok initially had 276 cups and 46 jars.
Now, let's calculate the number of cups and jars sold:
Number of cups sold = Initial number of cups - Remaining number of cups
= 276 - (2/3)(276)
= 276 - 184
= 92
Number of jars sold = Initial number of jars - Remaining number of jars
= 46 - (1/2)(46)
= 46 - 23
= 23
Therefore, the total number of cups and jars sold is 92 + 23 = 115.