Word Problems on Elimination Method

Q. Round 1: Car A and Car B start moving in opposite direction to each other from two different points which are 22.4 Km apart. They meet after 2 hours.

Round 2: Car A and Car B start from same point in same direction and after 3 hours, difference of their covered distance becomes 26.4 Km.

Given that speed of both cars remains same in both rounds and speed of car A > speed of car B.

Find the speed of Car A(in Km/hr).

Q. William is throwing a party for his math class and decides to visit Jones' Pi Bakery. There, cupcakes cost $$2$ and pies cost $$7.5$. William bought a total of $20$ items. In all, he spent $$73$. How many cupcakes and pies did he purchase?

1. $6,14$
2. $8,12$
3. $12,8$
4. $14,6$

Q. A minor league ballpark attracts $88$ fans and draws in $$553$ in revenue from ticket sales. A child's ticket costs $$4$ and an adult's ticket is $$7$. How many of each type of ticket were sold?

1. $18$ children, $70$ adults
2. $67$ children, $21$ adults
3. $21$ children, $67$ adults
4. $70$ children, $18$ adults

Q.

Walter earns a year-end bonus of $\$5000$ and puts it in $3$ one-year investments that pay $\$243$ in simple interest.

Part is invested at $3\%$, part at $4\%$ and part at $6\%$.

There is $\$1500$ more invested at $6\%$ than at $3\%$.

Find the amount invested at each rate.

Q. When two fluids of different densities having volume of $4\text{L}$ and $5\text{L},$ respectively are mixed, it results in a mass of $53\text{pounds}.$ When the same two liquids are mixed in the reversed proportion, the resulting mass is increased by $2\text{pounds}.$ Find the ratio of densities of the two liquids.

1. $7:9$
2. $7:5$

Q.

How do you calculate interest per year$?$

Q. Layla traveled a total distance of $450\text{miles}$ initially by car with an average speed of $60\text{miles/hour,}$ and subsequently by train with an average speed of $110\text{miles/hour.}$ Total time required is $5$ hours. Find the time spent on the train.

1. $3$ hours
2. $6$ hours
3. $9$ hours

Q. When a number is subtracted from a number with digits as the reverse of the original number, we get 27. The sum of the digits is 7. The original number is

Q.

Let's assume Sarah's father invests $$12,000$ in interest-bearing accounts, with a portion at $3.2$% and the remainder at $2.6$%. Total investment revenue (interest) for the year is $$369$. At each rate, how much money did Sarah's father put in?

1. 
   $3500,8500$
2. 
   $2500,9500$
3. 
   $4500,7500$
4. 
   $5500,6500$

Q. A principal amount of $\$8,000$ was partly invested in two schemes with an annual interest rate of $4\%$ and $5\%,$ respectively. At the end of the year, the total interest is $\$350.$ Find the ratio of investment.

1. $5:3$
2. $5:8$
3. $4:8$
4. $3:8$

Q. The perimeter of the rectangle is ${16}^{\prime \prime }.$ The length of the rectangle is one less than two times its height. What are the dimensions of the rectangle?

1. $4^{\prime \prime }$ and $4^{\prime \prime }$
2. $5^{\prime \prime }$ and $3^{\prime \prime }$
3. $3^{\prime \prime }$ and $2^{\prime \prime }$
4. $7^{\prime \prime }$ and $4^{\prime \prime }$