Three-Item-Menu is a restaurant thats sells only burgers, french fries, and soft drinks. One day, exactly 120 customers made a purchase. Half of the customers purchased at least a burger, 1 4 of the customers purchased at least french fries, but 1 3 of the customers purchased only a soft drink. Of the customers who bought a burger, 4 5 of them bought at least one other item. How many customers purchased a burger and soft drink but not french fries?

Let a be the number of customers who purchased a hamburger only. Let b be the number of customers who purchased french fries only. Let c be the number of customers who purchased a soft drink only. Let d be the number of customers who purchased a hamburger and french fries but not a soft drink. Let k be the number of customers who purchased french fries and a soft drink but not a hamburger. Let m be the number of customers who purchased a hamburger and a soft drink but not french fries. Let n be the number of customers who purchased a hamburger, french fries and a soft drink. We know that 120 customers made a purchase, so a + b + c + d + k + m + n = 120 . . . 1 We are given that half of the customers purchased a hamburger, so 1 2 × 120 = 60 customers purchased a hamburger. These customers may have also purchased french fries or a soft drink or both or neither. This tells us that a + d + m + n = 60 . . . 2 We are given that 1 4 of the customers purchased french fries, so 1 4 × 120 = 30 customers purchased french fries. These customers may have also purchased a hamburger or a soft drink or both or neither. This tells us that b + d + k + n = 30 . . . 3 We are given that 1 3 of the customers purchased only a soft drink, so 1 3 × 120 = 40 customers purchased only a soft drink. Therefore, c = 40 . We are given that, of the customers who bought a hamburger, 4 5 bought at least one other item. So, 4 5 of the 60 customers who purchased a hamburger bought at least one other item. In other words, 4 5 × 60 = 48 also bought french fries, a soft drink or both. Therefore, d + m + n = 48 . . . 4 Subtracting equation ( 4 ) from equation ( 2 ) , we see that a = 12 Substituting a = 12 and c = 40 into equation ( 1 ) , we have 12 + b + 40 + d + k + m + n = 120 thus b + d + k + m + n = 68 , or ( b + d + k + n ) + m = 68 . From equation ( 3 ) we know b + d + k + n = 30 , and so 30 + m = 68 , thus m = 38 . Therefore, 38 customers purchased a hamburger and soft drink but not french fries. We have determined what was required and can stop here. We do not need to solve for the remaining variables. It actually turns out that in this problem there is not enough information given to determine the values of all of the remaining variables.

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7th CBSE

IMPORTANT

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If $\frac{7}{3}$ of a number is $13$ more than $\frac{1}{6}$ of the number, find the number

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Important Questions on Simple Equations

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 25

Manu is solving problem he got in the quiz competition. Sum of three whole numbers is $104$ . Two of the numbers have difference of $8$ . Two of the numbers are the same.

What is the largest number in the set?

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7th CBSE

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Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 26

Two wooden blocks of the same length is arranged to have an overlap of each other by $8 cm$ . The length of the whole arrangement is $30 cm$ .

Question Image

Find the length of a wooden block.

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 27

Sita has

₹ 750

₹ 50

and

₹ 20

7

of the notes were

₹ 50

. How many notes is that of

₹ 20

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 28

A large family booked two rooms in a hotel. The charge per day for one room is $₹ 4000$ . One room is given to one person and rest of people who stay in the room is charged $₹ 500$ per day.

The family paid $₹ 14, 500$ for one day stay. How many members were there in the family?

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7th CBSE

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Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 29

Tara thought of a number. She added

10

to the number and then took its half. The answer she got is

\frac{2}{3}

of the number she thought of. What is the number Tara thought of?

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 30

Three-Item-Menu is a restaurant thats sells only burgers, french fries, and soft drinks. One day, exactly

120

customers made a purchase. Half of the customers purchased at least a burger,

\frac{1}{4}

of the customers purchased at least french fries, but

\frac{1}{3}

of the customers purchased only a soft drink. Of the customers who bought a burger,

\frac{4}{5}

of them bought at least one other item. How many customers purchased a burger and soft drink but not french fries?

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 31

The value of the ones digit of a

3

-digit number is three times the hundreds digit and twice the tens digit. Find the number.

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7th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VII>Chapter 4 - Simple Equations>Exercise>Q 33

Sumit has some red balls and some blue balls. The number of blue balls is

4

more than

4

times the number of red balls. Find the number of red balls, if the number of blue balls is

24

If 73 of a number is 13 more than 16 of the number, find the number

Important Questions on Simple Equations

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If $\frac{7}{3}$ of a number is $13$ more than $\frac{1}{6}$ of the number, find the number