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Chapter 5: Q. 399 (page 683)

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

The sum of two numbers is 鈭�24. One number is 104 less than the other. Find the numbers.

Short Answer

Expert verified

The number are40and-64.

Step by step solution

01

Step 1. Given Information

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

The sum of two numbers is 鈭�24. One number is 104 less than the other. Find the numbers.

02

Step 2. Let x=One Numbery=Second number.

The sum of two numbers is 鈭�24.

x+y=-24鈥�鈥�鈥�鈥�鈥�鈥�Equation1

One number is 104 less than the other.

y=x-104鈥�鈥�鈥�鈥�鈥�鈥�Equation2

03

Step 3. Using substitution method to solve the equation.

Putting the value of yfrom the Equation 2 in Equation 1

x+x-104=-242x-104=-24Add104onbothside2x-104+104=-24+1042x=80Divideby2onbothside22x=802x=40

04

Step 4. Putting the value of x in Equation 2.

y=40-104y=-64

The numbers are40and-64.

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