A and B go shopping.The total of money they have is 142.20$.B has three times of the amount A has,minus 56.20$. How much does A have and how much does B have?

Question

I cant seem to answer this questions and am unsure about the steps

Answer 1

Identify the unknowns we need to find: How much does A have and how much does B have?

 

Let A = the amount of money that A has

Let B = the amount of money that B has

 

We have two unknowns, so we need two equations that relate the unknowns:

1. The total of money they have is $142.20:  A + B = $142.20
2. B has three times the amount A has,minus $56.20:  B = 3A-$56.20

Substitution:

A+B = $142.20

B = $142.20 - A

 

Now substitute $142.20-A in place of B in equation 2

B = 3A-$56.20                     [Equation 2]

$142.20 - A = 3A - $56.20    [Substituted $142.20-A in place of B]

 

Solve for A:

$142.20 + $56.20 = 4A

$198.40 = 4A

$49.60 = A

 

Solve for B:

B = $142.20 - A

B = $142.20 - 49.60

B = $92.60

 

Check:

A+B = $142.20

$49.60 + $92.60 = $142.20

$142.20 = $142.20                    [Check!]

 

B = 3A-$56.20

$92.60 = (3)(49.60) - $56.20

$92.60 = $148.80 - $56.20

$92.60 = $92.60                        [Check!]

 

Answer 2

a+b = 142.40

b= 3a-56.20

replacing b in the first equation, we obtain:

a+3a-56.20 = 142.40

4a = 198.60

Then a = 49.65

b= 142.40 - 49.65 = 92.75