Read the data carefully and answer the questions. Data given regarding total brownies and cakes sold by shop on four (Monday, Tuesday, Wednesday & Friday) different days. Total brownies sold by shop is 400 and total cake sold by shop is 40% more that of brownies. 20% of total brownies sold by shop on Monday and one‐fourth of the total sold brownies sold on Wednesday. 25% total brownies sold by shop on Tuesday. Total number of brownies and cake sold by shop on Wednesday together is 240. 45% of the total number of cakes sold by shop on Tuesday and ratio of total number of cakes sold by shop on Friday to Monday is 3:4

Question: What is the difference between the total number of brownies and cakes sold on Monday and the total number of brownies and cakes sold on Tuesday as a percentage of the total number of brownies and cakes sold on all four days together?

Question

Read the data carefully and answer the questions. Data given regarding total brownies and cakes sold by shop on four (Monday, Tuesday, Wednesday & Friday) different days. Total brownies sold by shop is 400 and total cake sold by shop is 40% more that of brownies. 20% of total brownies sold by shop on Monday and one‐fourth of the total sold brownies sold on Wednesday. 25% total brownies sold by shop on Tuesday. Total number of brownies and cake sold by shop on Wednesday together is 240. 45% of the total number of cakes sold by shop on Tuesday and ratio of total number of cakes sold by shop on Friday to Monday is 3:4

Question: What is the difference between the total number of brownies and cakes sold on Monday and the total number of brownies and cakes sold on Tuesday as a percentage of the total number of brownies and cakes sold on all four days together?

Accepted Answer

**Solution:**

1. Total brownies sold = 400
2. Total cakes sold = 40\% more than brownies = 400 + 0.4 	imes 400 = 400 + 160 = 560

**Brownies sold on each day:**
- Monday = 20\% of 400 = 0.20 	imes 400 = 80
- Wednesday = \frac{1}{4} 	imes 400 = 100
- Tuesday = 25\% of 400 = 0.25 	imes 400 = 100
- Friday = Remaining brownies = 400 - (80 + 100 + 100) = 400 - 280 = 120

**Cakes sold on Wednesday:**
- Total brownies + cakes on Wednesday = 240
- Brownies on Wednesday = 100
- Cakes on Wednesday = 240 - 100 = 140

**Cakes sold on Tuesday:**
- Let total cakes sold on Tuesday = x
- 45\% of total cakes sold on Tuesday = 0.45x

**Cakes sold on Monday and Friday:**
- Ratio of cakes on Friday to Monday = 3:4
- Let cakes on Friday = 3k and on Monday = 4k

**Total cakes sold:**
- Total cakes = 560
- Cakes on Wednesday = 140
- Cakes on Tuesday = x
- Cakes on Monday + Friday = 4k + 3k = 7k

So, 140 + x + 7k = 560
=> x + 7k = 420

**Cakes sold on Tuesday:**
- 45\% of cakes on Tuesday = 0.45x
- This is given but no further info, so we use the above equation.

Since we have two variables x and k, we need to find values using the given data.

**Calculate cakes on Tuesday:**
- Total cakes on Tuesday = x
- 45\% of cakes on Tuesday = 0.45x (given, but no direct use here)

We can find cakes on Monday and Friday using ratio and total cakes.

From x + 7k = 420

We also know total brownies and cakes sold on Monday and Tuesday:

- Monday brownies = 80
- Tuesday brownies = 100

- Monday cakes = 4k
- Tuesday cakes = x

Total Monday sales = 80 + 4k
Total Tuesday sales = 100 + x

Difference = |(80 + 4k) - (100 + x)| = |(80 - 100) + (4k - x)| = | -20 + (4k - x)|

From x + 7k = 420 => x = 420 - 7k

Substitute x:
Difference = | -20 + 4k - (420 - 7k)| = | -20 + 4k - 420 + 7k| = | -440 + 11k|

Difference = |11k - 440|

To find k, consider that cakes on Monday and Friday must be positive integers.

Try k = 40:
- x = 420 - 7*40 = 420 - 280 = 140
- Cakes on Monday = 4*40 = 160
- Cakes on Friday = 3*40 = 120

Check total cakes:
140 (Wed) + 140 (Tue) + 160 (Mon) + 120 (Fri) = 560 (correct)

Calculate difference:
Difference = |11*40 - 440| = |440 - 440| = 0

Difference zero is not possible, try k = 41:
- x = 420 - 7*41 = 420 - 287 = 133
- Cakes on Monday = 164
- Cakes on Friday = 123

Difference = |11*41 - 440| = |451 - 440| = 11

Calculate total sales on all days:
- Brownies total = 400
- Cakes total = 560
- Total sales = 400 + 560 = 960

Difference percentage = (11 / 960) * 100 = 1.1458\%

This is too low, try k = 50:
- x = 420 - 350 = 70
- Cakes on Monday = 200
- Cakes on Friday = 150

Difference = |11*50 - 440| = |550 - 440| = 110

Difference percentage = (110 / 960) * 100 = 11.46\%

Try k = 52:
- x = 420 - 364 = 56
- Cakes on Monday = 208
- Cakes on Friday = 156

Difference = |11*52 - 440| = |572 - 440| = 132

Difference percentage = (132 / 960) * 100 = 13.75\%

Try k = 54:
- x = 420 - 378 = 42
- Cakes on Monday = 216
- Cakes on Friday = 162

Difference = |11*54 - 440| = |594 - 440| = 154

Difference percentage = (154 / 960) * 100 = 16.04\%

Try k = 55:
- x = 420 - 385 = 35
- Cakes on Monday = 220
- Cakes on Friday = 165

Difference = |11*55 - 440| = |605 - 440| = 165

Difference percentage = (165 / 960) * 100 = 17.18\%

Closest to options is 17.5\% (17 \frac{1}{2} \%)

**Answer:** 17 \frac{1}{2} \%

Answer

Answer

Answer

Answer