Finding the Unknown

Solve these equations and check the solutions. (a) $3x - 10 = 35$ (b) $5s = 3s$ (c) $3u - 7 = 2u + 3$ (d) $4(m + 6) - 8 = 2m - 4$ (e) $\frac{u}{15} = 6$

Frame an equation that has no solution. [Hint: 4 more than a number, and 5 more than a number can never be equal!]

Write 5 equations whose solution is $x = -2$.

Find the value of each unknown: (a) $2y = 60$ (b) $-8 = 5x - 3$ (c) $-53w = -15$ (d) $13 - z = 8$ (e) $k + 8 = 12 - k$ (f) $7m = m - 3$ (g) $3n = 10 + n$

I am a 3-digit number. My hundred's digit is 3 less than my ten's digit. My ten's digit is 3 less than my unit's digit. The sum of all the three digits is 15. Who am I?

The weight of a brick is 1 kg more than half its weight. What is the weight of the brick?

One quarter of a number increased by 9 gives the same number. What is the number?

Given $4k + 1 = 13$, find the values of: (a) $8k + 2$ (b) $4k$ (c) $k$ (d) $4k - 1$ (e) $-k - 2$

Fill in the blanks with integers. (a) $5 \times \_\_\_ - 8 = 37$ (b) $37 - (33 - \_\_\_) = 35$ (c) $-3 \times (-11 + \_\_\_) = 45$

Ranju is a daily wage labourer. She earns ₹750 a day. Her employer pays her in 50 and 100 rupee notes. If Ranju gets an equal number of 50 and 100 rupee notes, how many notes of each does she have?

A taxi driver charges a fixed fee of ₹800 per day plus ₹20 for each kilometer traveled. If the total cost for a taxi ride is ₹2200, determine the number of kilometres traveled.

The sum of two numbers is 76. One number is three times the other number. What are the numbers?

In a restaurant, a fruit juice costs ₹15 less than a chocolate milkshake. If 4 fruit juices and 7 chocolate milkshakes cost ₹600, find the cost of the fruit juice and milkshake.

Given $28p - 36 = 98$, find the value of $14p - 19$ and $28p - 38$.

Write 4 equations whose solution is $u = 6$.

The Bakhshali Manuscript (300 CE) mentions the following problem. The amount given to the first person is not known. The second person is given twice as much as the first. The third person is given thrice as much as the second; and the fourth person four times as much as the third. The total amount distributed is 132. What is the amount given to the first person?

The height of a giraffe is two and a half metres more than half its height. How tall is the giraffe?

A number increased by 36 is equal to ten times itself. What is the number?

There are some children and donkeys on a beach. Together they have 28 heads and 80 feet. How many donkeys are there? How many children are there?