two part-time jobs for a total of 34 hours a week.JobA pays$6.40 per hour, and JobB pays$7.30 per hour.How many hrs did she work at each job to make $234.70.

Question

i need job A and B

Answer 1

You can use a system of equations to solve the problem.

 

Step 1: Select what the variables will mean:

a=hours at job A

b=hours at job B

 

Step 2: Set up Equations:

Total hours:  a+b=34  (hours at job A plus hours at job B is equal to the total hours of 34)

Total wages: 6.40a + 7.30b = 234.70 (wage*hours at job A plus wage*hours at job B equals the total earned of 234.70)

 

To solve now, use substitution to solve for one variable and then use that answer to put back to get the other.  Here we go:

 

Step 3: Use a+b=34.  Solve for a.  a=34-b (I subtracted b from both sides to get a by itself).

Step 4: Now that we know that a=34-b, we can substitute that into the second equation-- 6.40a + 7.30b = 234.70

 

6.40(34-b)+7.30b=234.70 (now we have just "b" and can find what b is equal to).  So now we get,

 

217.60-6.40b + 7.30b = 234.70, next combine like terms on the right side, (-6.40+7.30)

 

217.60 + 0.9b  = 234.70, now subtract 217.60 from both sides to get b by itself (234.70-217.60)

 

0.9b = 17.1, now solve for b by dividing each side by 0.9,

 

b=17.1/0.9 = 19 (This means 19 hours worked at job b)

 

STEP 5: Now use that number 19 to put back into one of the original equations. 

 

I will use a + b = 34 since it is an easier equation to solve. So using b=19, now we solve for a:

 

a + 19 =34.  Solve for a by subtracting 19 from both sides:

 

a  = 34-19,

 

a= 15, so 15 hours worked at job A

 

FINAL ANSWER:  a= 15 hours, b= 19 hours,

 

So student worked 15 hours at job A and 19 hours at job B