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Evaluating Algebraic expressions with variables word problems

How do you evaluate the expression?

To evaluate an expression, we substitute the value for each variable, and then apply the operations.

Example: Evaluate 2(5y + 10) for y = 8.

We put y = 8 in 2(5y + 10), we get

2(5y + 10) = 2[5(8) + 10] = 2[40 + 10] = 2[50] = 2 × 50 = 100 (Answer)

We can have a good understanding of evaluating expressions with variables with the help of following examples:

 

Example: The price Regina pays to visit the vet’s clinic is calculated according to the formula 20 + 50n. Here n is the number of times she visits him in a year. This time it was 2. What was the cost of his visit?

Equation here says:  20 + 50n

= 20 + (50.n)

= 20 + (50 × 2)

= 20 + 100

= $120 (Answer)

The expression 10g, tells the number of miles a car can travel using g liters of gasoline.

How far can this car travel on 10\frac{1}{2}  litres of gasoline?

 

Solution: 10g is the expression

= 10. 10\frac{1}{2}

= 10 × \frac{21}{2}

= 5 × 21

= 105 miles (Answer)

  1. The expression is 3f + 23, where f is 10. What is the value of the expression?
  2. What is the pocket money Hilly receives in a week if she gets 5w + 12, where w is $10?

  1. Kim runs a food truck. The expression 25s + 2hgives the cost of s sandwiches and h hot dogs. Find the cost of 3 sandwiches and 7 hot chocolates.

 

  1. In a School sports day, the number of points the 8th grade team scores is given by 3x + 2y + 1z, xis the red team; y is yellow team, and z is the blue team. What is the total number of points scored by 10th graders when red scores 3 three points, yellow 5 points, and blue 2 points?

  1. The expression 7w + 200 litres are the water level which drops in a particular reservoir in a day. Calculate the water level if today is the 5th day.
Answer key
  1. $53
  2. $62
  3. $20.75
  4. 21 points
  5. 235 litres

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