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Chapter 5: Q. 347 (page 679)

In the following exercises, translate to a system of equations and solve.

The sum of two number is 55. One number is 11 less than the other. Find the numbers.

Short Answer

Expert verified

Two numbers are 22 and 33.

Step by step solution

01

Step 1. Assumption

Assume to numbers to bex,y.

02

Step 2. Form system of equations

  • The sum of numbers is 55. So, the equation will be x+y=55.
  • xis 11 less than y. So, the equation will bex=y-11.
  • So, the system of equation will bex+y=55x=y-11
03

Step 3. Find the value of y.

  • Substitute x=y-11into the first obtained equation.

(y-11)+y=552y-11=552y=66y=33

  • So, the value of yis 33.
04

Step 4. Determine the value of x.

  • Substitute x=33into the first obtained equation.

x+33=55x=22

  • So, two numbers are 22 and 33.
05

Step 5. Checking

  • Substitute x=22,y=33into both the constructed equations and check if the equations are satisfied.

22+33=?5555=5522=?33-1122=22

  • As both the equations are satisfied, the solution is verified.

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