word problem

Question

4 plates and 5 bowls cost $103.60 altogether.  8 plates and 3 bowls costs $134.40 altogether.  how much less does each bowl cost than each plate?

 

Answer 1

Step 1: Create Equations

4p + 5b  = 103.60  -- eq(1)

8p + 3b  = 134.40 -- eq(2)

 

Step 2: Multiply equation 1 by 4

8p + 10b = 207.20 -- eq(3)

 

Step 3: Subtract equation 2 from equation 3

 8p + 10b = 207.20

-8p + 3b = 134.40

Therefore, 7b =  72.8

b = 10.4

 

Step 4: Put value of b in equation 1 to find value of p

4p  + 5(10.4) = 103.60

p = 12.9

 

Step 5: Look carefully at the question and calculate answer

how much less does each bowl cost than each plate?

bowl costs 10.4 and plate costs 12.9

Therefore answer is 12.9 - 10.4 = 2.5

 

Step 6: Write Answer

Each Bowl cost $2.5 less than each plate.