# BECE 2022: 2 Tricky Word Problem Questions On Linear Equations

Generally, BECE questions are set such that they are unambiguous. Usually, the questions are straightforward. In Mathematics, solving word problems is one of the greatest challenges for students. Ahead of the 2022 BECE, let us go through some two tricky word problem questions on linear equations and how to go about it.

## Eunice is three times as old as Mavis. The sum of their ages is 60. How old is each of them?

### You Can Solve It Before Checking Out The Solutions To Try Yourself. If you can solve it correctly by yourself, then you have a higher chance of getting 1 in Mathematics.

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This is a fine question. To make your solutions more simplified and less complex, we can represent the two individual ages with variables. However, you can go ahead and use the names provided.

- Let Eunice’s age be
**e** - Let Mavis’ age be
**m**

Now, we have to translate the statements and conditions in the question into mathematics language.

- Eunice is three times as old as Mavis

## ⇒e=3m and m=m

- The sum of their ages is 60.

## ⇒3m+m=60

Now that we have derived this mathematical linear equation, we now solve for m,

## ⇒3m+m=60

## ⇒4m=60

## ⇒4m/4=60/4

## ⇒m=15

If Mavis is 15 years old, then Eunice’s age is

## ⇒e=3m

## ⇒e=3(15)

## ⇒e=45

Therefore, Mavis’s age is 15, and Eunice’s age is 45.

After solving, you can go ahead to check if indeed the answer you derived satisfies the conditions given. So, in the question, we were told that the sum of the two ages is 60. This is very accurate since (45+15=60).

## The sum of three numbers is 27. The second number is three times the first, while the third is twice the first. Find the average

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This is an interesting question. It is a combination of linear equations, statistics, and word problems. Once again, we approach this question by representing all three numbers with any variables.

- Let
be the first number**x** be the second number**y**-
be the 3rd number.**z**

Now, we convert the word problem into a mathematical equation.

- The sum of three numbers is 27

## ⇒*x*+*y*+**z**=27

*x*

*y*

**z**

- The second number is three times the first

## ⇒*y*=3 X *x=3x*

*y*

*x=3x*

- the third is twice the first

## ⇒**z**=2 X** x=2x**

**z**

**x=2x**

Now we make the necessary substitutions and find the values of x, y, and z.

## ⇒**x**+3x+2x=27

## ⇒6x=27

## ⇒x=27/6

## ⇒x=9/2=4.5

## ⇒y=3x=3(4.5)=13.5

## ⇒z=2x=2(4.5)=9

We are required to find the average. The average is the same as finding the mean. The mean is the sum of all the observations divided by the total number of observations

** x̄=(4.5+13.5+9)/3**

**x̄=(4.5+13.5+9)/3**

**=27/3**

**=9**

So the average is 9.

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