Question

Here are some strategies that you can use in solving word problems:
(1) Look for a pattern, (2) Make an organized list/ make a table, (3) Create an equation, and (4) Work backwards.

A. Find the two numbers which has a sum of 12 and a difference of 48 between their squares. What strategy did you use (choose from the example strategies)?











B. Joshua is thinking of a number. If you triple it, and subtract 12, you obtain 18. What is Joshua’s number? What strategy did you use (choose from the example strategies)?











C. How long will it take for a car traveling 75 miles per hour to catch up to another car traveling 65 miles per hour if the slower car begins one hour before the faster car? What strategy did you use (choose from the example strategies)?

Answer 1

A.

$x + y = 12 \\ {x}^{2} - {y}^{2} = 48\\(x - y)(x + y) = 48 \\ (12)(x - y) = 48 \\ x - y = 4 \\ x + y + x - y = 12 + 4 \\ 2x = 16 \\ x = 8$

B.

$3x - 12 = 18 \\ 3x =18 + 12 \\ 3x = 30 \\ x = 10$

C.

$LCM(75,65) = 975$

It will take 975 km

$975km - 65km = 910km \\ (910km / t ) = (65km/h) \\ t = (910/65)h\\ t = 14h$

Answer 2

Given The two numbers which has a sum of 12 and a difference of 48 between their squares.  

To Find :  strategy used

Find the numbers

Solution:

strategy used :  Create an equation,

Assume that one number  is  x  

and other is  12 - x

difference of 48 between their squares.  

x² - (12 - x)²  = 48

=> x² - 144 - x² + 24x  = 48

=> 24x = 192

=> x = 8

12 - x = 4

Numbers are  8 and 4

Create an Equation

Number = N

3N - 12  = 18

=> 3N = 30

=> N = 10

Number is 10

Distance Covered by 1 st car in 1 hr = 65 * 1  = 65 miles  per hrs

Assume that Another car takes t hrs to catch up

Distance covered by faster in t hrs  = 75t miles

Distance covered by slower in t hrs  = 65t miles

Create an Equation

75t - 65t  = 65

=> 10t = 65

=> t = 6.5 hrs

Learn More:

By using variable A and B write any two equation whose solution will be (0, 2)​

brainly.in/question/37927696