Chapter 1.7, Problem 9P

To determine

To calculate: Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given.Elena has one and half times as much money as Ramon. Together they have$225. How much money does each have? Choices foe Ramon's amount: 80, 90, 95.

Answer to Problem 9P

The amount of money Ramon has is $a=90$ and the amount of money Elena has

  $\frac{3}{2}a=\frac{3}{2}\left(90\right)=135$

Explanation of Solution

Given information:Elena has one and half times as much money as Ramon and together they have$225.

Calculation:

Step 1: Here we have two unknowns.

Step 2: Let $a$ be the amount of money that Ramon has and $\frac{3}{2}a$ the amount of money that Elena has.

Step 3: As given, total money they have is $225, so $a+\frac{3}{2}a=225$

Step 4: Choices for $a$ are given as 80, 90, 95.

$a$	$a+\frac{3}{2}a=225$	True / False
80	$80+\frac{3}{2}*80=225$	False
90	$90+\frac{3}{2}\left(90\right)=225$	True
95	$95+\frac{3}{2}\left(95\right)=225$	False

From above table we can say that the amount of money Ramon has is $a=90$ and theamount of money Elena has $\frac{3}{2}a=\frac{3}{2}\left(90\right)=135$

Step 5: Now we verify the answer

Elena has one and half time as much money as Ramon has $\frac{3}{2}\left(90\right)=135$ , which is correct

Total money they have $225, so $90+135=225$ , which is also correct.