Chapter 1.7, Problem 4P

To determine

To calculate: Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given.One number is four times another number. The larger number is also 87 more than the smaller number. Find the numbers.

Choices for the smaller number: 29, 30, 33

Answer to Problem 4P

smallest number $a=29$ and larger number $4a=116$

Explanation of Solution

Given information: One number is four times another number and the larger number is also 87 more than the smaller number.

Calculation:

Step 1: Here we have two unknowns.

Step 2: Let $a$ be the smaller number, so that $4a$ is larger number.

Step 3: As given, larger number is 87 more than the smaller number such that $4a=a+87$

Step 4: Choices for $a$ are given as 29, 30, 33

$a$	$4a=a+87$	True / False
29	$4\left(29\right)=29+87=116$	True
30	$4\left(30\right)=30+87=117$	False
33	$4\left(33\right)=33+87=120$	False

From above table we can say that smallest number $a=29$ and larger number $4a=116$

Step 5: Now we verify the answer

one number is four times of another number: $4*29=116$ , which is correct

Larger number is 87 more than the smaller number: $39+87=116$ , which is also correct.