Sure, let's solve this step by step:

Step 1: Understand the problem
The problem tells us that Daniel bought 500 sweets, which changed the ratio of Colin's sweets to Daniel's sweets from 1:7 to 6:67. We need to find out how many sweets Colin had initially.

Step 2: Set up the equations
Let's denote the initial number of sweets Colin had as C and the initial number of sweets Daniel had as D. We know from the problem that:

C/D = 1/7 (equation 1)

After Daniel bought 500 more sweets, the ratio became:

C/(D+500) = 6/67 (equation 2)

Step 3: Solve the equations
We can start by solving equation 1 for C:

C = D/7

Substitute C in equation 2:

D/7 / (D+500) = 6/67

Cross multiply:

67D = 42D + 21000

Solve for D:

25D = 21000

D = 840

Substitute D = 840 into equation 1:

C = 840/7

C = 120

So, Colin initially had 120 sweets.

Question

Sure, let's solve this step by step:

Step 1: Understand the problem
The problem tells us that Daniel bought 500 sweets, which changed the ratio of Colin's sweets to Daniel's sweets from 1:7 to 6:67. We need to find out how many sweets Colin had initially.

Step 2: Set up the equations
Let's denote the initial number of sweets Colin had as C and the initial number of sweets Daniel had as D. We know from the problem that:

C/D = 1/7  (equation 1)

After Daniel bought 500 more sweets, the ratio became:

C/(D+500) = 6/67  (equation 2)

Step 3: Solve the equations
We can start by solving equation 1 for C:

C = D/7

Substitute C in equation 2:

D/7 / (D+500) = 6/67

Cross multiply:

67D = 42D + 21000

Solve for D:

25D = 21000

D = 840

Substitute D = 840 into equation 1:

C = 840/7

C = 120

So, Colin initially had 120 sweets.

Knowee AI · Accepted Answer