Introduction to Linear Polynomials | Exercise 2.2

Question 5

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

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Solution
Understand the Question
  • Let the number of ₹55 coins be xx.
  • Since Ruby has 33 times as many ₹22 coins as ₹55 coins, the number of ₹22 coins is 3x3x.
  • The total value of money is the sum of the values of both types of coins: 5(x)+2(3x)=885(x) + 2(3x) = 88.
  • We solve this linear equation for xx to find the count of each denomination.

Step 1 · Form and Solve the Equation

Let the number of five-rupee coins be xx. Then, the number of two-rupee coins is 3x3x.Diagram 1

According to the question

5x+2(3x)=885x+6x=8811x=88x=8811x=8\begin{aligned} 5x + 2(3x) &= 88 \\[0.6em] 5x + 6x &= 88 \\[0.6em] 11x &= 88 \\[0.6em] x &= \dfrac{88}{11} \\[0.6em] x &= 8 \end{aligned}

Step 2 · Find the Number of Coins of Each Type

Substitute x=8x = 8 to find the count of each coin type:

Number of five-rupee coins=x=8\text{Number of five-rupee coins} = x = 8

Number of two-rupee coins=3x=3×8=24\begin{aligned} \text{Number of two-rupee coins} &= 3x \\[0.6em] &= 3 \times 8 \\[0.6em] &= 24 \end{aligned}
Answer

Number of ₹55 coins =8= 8, Number of ₹22 coins =24= 24

Common Mistakes
  • Equating Coin Count to Value: Setting x+3x=88x + 3x = 88 by forgetting to multiply each coin type by its monetary value (₹55 and ₹22).
  • Reversing the Multiplier: Setting the number of five-rupee coins as 3x3x and two-rupee coins as xx, which inverts the given relationship.

More questions in Exercise 2.2

Q1

Find the value of the linear polynomial 5x−35x - 3 if:

(i) x=0x = 0

(ii) x=−1x = -1

(iii) x=2x = 2

Q2

Find the value of the quadratic polynomial 7s2−4s+67s^2 - 4s + 6 if:

(i) s=0s = 0

(ii) s=−3s = -3

(iii) s=4s = 4

Q3

The present age of Salil's mother is three times Salil's present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Q4

The difference between two positive integers is 63. The ratio of the two integers is 2:52 : 5. Find the two integers.

Q5

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

Q6

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Q7

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

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