Word Problems on Solving Algebraic Equations

Q.

The sum of three numbers is $123$. If the ratio between first and second number is $2:5$ and that of between second and third is $3:4$ then find the difference between second and third number.

Q. Sana had caramel and orange flavor candies, the number of caramel candies was 10 more than the number of orange flavor candies. If she has 100 candies in total, then the number of caramel candies is
.

Q. Kate has $\$500$ as currency notes in the denominations of $\$50$ and $\$20$. The ratio of the number of $\$50$ notes and $\$20$ notes is $3:5$. Then, the number of $\$50$ notes is and the number of $\$20$ notes is .

Q.

Because it is so popular, a store increases the cost of a toy by $\$3.49$.

The new cost of the toy is $\$9.84$.

Write an equation that represents the situation and find the solution.

Use $c$ to represent the original cost of the toy.

Q. Students in a class planted 100 trees. They planted some fruit trees and some non-fruit trees. The number of non-fruit trees was one more than twice the number of fruit trees. How many fruit trees and non-fruit trees did they plant?

1. $33$ and $68$
2. $34$ and $67$
3. $33$ and $67$
4. $35$ and $68$

Q. Ice creams are on a sale! Each ice cream costs $\$2$ less than the original price. David buys 3 of them and it costs him $\$18.$ Find the original price of each ice cream.

1. $\$4$
2. $\$5$
3. $\$15$
4. $\$8$

Q. Lucas orders some tennis balls from online shopping. Each tennis ball costs $\$20$ and the shipping fee is $\$5$ regardless of the number of tennis balls. If Lucas spent a total of $\$105,$ how many tennis balls did he order?

1. $5$
2. $4$
3. $10$
4. $15$

Q. John saves $\$10$ every month in his saving account. He withdrew $\$50$ once to go shopping. Now he has $\$250$ in his account. How long he has been saving?
months

Q. Jackson bought a book for $\$10$ and 5 pens. He spent a total of $\$85$. Find the cost of each pen?
$