SOLUTION: I have a real hard time with word problems. I can't figure this one out. Eric is in charge of ordering the centerpieces for a school awards banquet. There are three types, which

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Question 6651: I have a real hard time with word problems. I can't figure this one out.
Eric is in charge of ordering the centerpieces for a school awards banquet. There are three types, which cost $22, $37, and $48. He needs to order some of each for a total of 35 centerpieces and a total cost of $1355. He needs 6 fewer of the $22 centerpieces than of the $37 centerpieces. How many $48 centerpieces does he need to order?
Any help will be appreciated.
Thanks!
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
Total number of centerpieces=35(given)
"He needs 6 fewer of the $22 centerpieces than of the $37 centerpieces."
now let number of $37 pcs be x.
then number of $22 pcs is (x-6)
then number of $48 pcs=35-x-(x-6)=35-x-x+6=(41-2x)


given that total cost is $1355
then cost of all the $37 pcs=37(x) dollars
cost of all the $22 pcs=22(x-6)dollars
cost of all the $48 pcs=48(41-2x) dollars


then total cost is equal to sum of the above
1355=37(x)+22(x-6)+48(41-2x)


Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=13.
  • Graphical form: Equation 1355=37%2A%28x%29%2B22%2A%28x-6%29%2B48%2A%2841-2x%29 was fully solved.
  • Text form: 1355=37*(x)+22*(x-6)+48*(41-2x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1355=37%2A%28x%29%2B22%2A%28x-6%29%2B48%2A%2841-2x%29+%29
    For tutors: simplify_cartoon( 1355=37*(x)+22*(x-6)+48*(41-2x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 1355=highlight_red%28+37%2A%28highlight_red%28+x+%29%29+%29%2B22%2A%28x-6%29%2B48%2A%2841-2%2Ax%29.
Remove unneeded parentheses around factor highlight_red%28+x+%29
It becomes 1355=37%2Ahighlight_green%28+x+%29%2B22%2A%28x-6%29%2B48%2A%2841-2%2Ax%29.
Look at 1355=37%2Ax%2B22%2A%28x-6%29%2B48%2A%28highlight_red%28+41+%29-2%2Ax%29.
Moved 41 to the right of expression
It becomes 1355=37%2Ax%2B22%2A%28x-6%29%2B48%2A%28-2%2Ax%2Bhighlight_green%28+41+%29%29.
Look at 1355=highlight_red%28+37%2Ax%2B22%2A%28x-6%29%2B48%2A%28-2%2Ax%2B41%29+%29.
Moved these terms to the left highlight_green%28+-37%2Ax+%29,highlight_green%28+-22%2A%28x-6%29+%29,highlight_green%28+-48%2A%28-2%2Ax%2B41%29+%29
It becomes 1355-highlight_green%28+37%2Ax+%29-highlight_green%28+22%2A%28x-6%29+%29-highlight_green%28+48%2A%28-2%2Ax%2B41%29+%29=0.
Look at highlight_red%28+1355+%29-37%2Ax-22%2A%28x-6%29-48%2A%28-2%2Ax%2B41%29=0.
Moved 1355 to the right of expression
It becomes -37%2Ax-22%2A%28x-6%29-48%2A%28-2%2Ax%2B41%29%2Bhighlight_green%28+1355+%29=0.
Look at -37%2Ax-highlight_red%28+22%2A%28x-6%29+%29-48%2A%28-2%2Ax%2B41%29%2B1355=0.
Expanded term -22 by using associative property on %28x-6%29
It becomes -37%2Ax-highlight_green%28+22%2Ax+%29%2Bhighlight_green%28+22%2A6+%29-48%2A%28-2%2Ax%2B41%29%2B1355=0.
Look at -37%2Ax-22%2Ax%2Bhighlight_red%28+22+%29%2Ahighlight_red%28+6+%29-48%2A%28-2%2Ax%2B41%29%2B1355=0.
Multiplied numerator integers
It becomes -37%2Ax-22%2Ax%2Bhighlight_green%28+132+%29-48%2A%28-2%2Ax%2B41%29%2B1355=0.
Look at -37%2Ax-22%2Ax%2Bhighlight_red%28+132+%29-48%2A%28-2%2Ax%2B41%29%2Bhighlight_red%28+1355+%29=0.
Added fractions or integers together
It becomes -37%2Ax-22%2Ax%2Bhighlight_green%28+1487+%29-48%2A%28-2%2Ax%2B41%29=0.
Look at -37%2Ax-22%2Ax%2Bhighlight_red%28+1487+%29-48%2A%28-2%2Ax%2B41%29=0.
Moved 1487 to the right of expression
It becomes -37%2Ax-22%2Ax-48%2A%28-2%2Ax%2B41%29%2Bhighlight_green%28+1487+%29=0.
Look at -highlight_red%28+37%2Ax+%29-highlight_red%28+22%2Ax+%29-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Eliminated similar terms highlight_red%28+-37%2Ax+%29,highlight_red%28+-22%2Ax+%29 replacing them with highlight_green%28+%28-37-22%29%2Ax+%29
It becomes highlight_green%28+%28-37-22%29%2Ax+%29-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Look at %28-highlight_red%28+37+%29-highlight_red%28+22+%29%29%2Ax-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Added fractions or integers together
It becomes %28highlight_green%28+-59+%29%29%2Ax-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Look at %28highlight_red%28+-59+%29%29%2Ax-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Removed extra sign in front of -59
It becomes %28-highlight_green%28+59+%29%29%2Ax-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Look at highlight_red%28+%28-highlight_red%28+59+%29%29%2Ax+%29-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Remove unneeded parentheses around factor highlight_red%28+59+%29
It becomes -highlight_green%28+59+%29%2Ax-48%2A%28-2%2Ax%2B41%29%2B1487=0.
Look at -59%2Ax-highlight_red%28+48%2A%28-2%2Ax%2B41%29+%29%2B1487=0.
Expanded term -48 by using associative property on %28-2%2Ax%2B41%29
It becomes -59%2Ax%2Bhighlight_green%28+48%2A2%2Ax+%29-highlight_green%28+48%2A41+%29%2B1487=0.
Look at -59%2Ax%2Bhighlight_red%28+48+%29%2Ahighlight_red%28+2+%29%2Ax-48%2A41%2B1487=0.
Multiplied numerator integers
It becomes -59%2Ax%2Bhighlight_green%28+96+%29%2Ax-48%2A41%2B1487=0.
Look at -59%2Ax%2B96%2Ax-highlight_red%28+48+%29%2Ahighlight_red%28+41+%29%2B1487=0.
Multiplied numerator integers
It becomes -59%2Ax%2B96%2Ax-highlight_green%28+1968+%29%2B1487=0.
Look at -59%2Ax%2B96%2Ax-highlight_red%28+1968+%29%2Bhighlight_red%28+1487+%29=0.
Added fractions or integers together
It becomes -59%2Ax%2B96%2Ax%2Bhighlight_green%28+-481+%29=0.
Look at -59%2Ax%2B96%2Ax%2Bhighlight_red%28+-481+%29=0.
Removed extra sign in front of -481
It becomes -59%2Ax%2B96%2Ax-highlight_green%28+481+%29=0.
Look at -highlight_red%28+59%2Ax+%29%2Bhighlight_red%28+96%2Ax+%29-481=0.
Eliminated similar terms highlight_red%28+-59%2Ax+%29,highlight_red%28+96%2Ax+%29 replacing them with highlight_green%28+%28-59%2B96%29%2Ax+%29
It becomes highlight_green%28+%28-59%2B96%29%2Ax+%29-481=0.
Look at %28-highlight_red%28+59+%29%2Bhighlight_red%28+96+%29%29%2Ax-481=0.
Added fractions or integers together
It becomes %28highlight_green%28+37+%29%29%2Ax-481=0.
Look at highlight_red%28+%28highlight_red%28+37+%29%29%2Ax+%29-481=0.
Remove unneeded parentheses around factor highlight_red%28+37+%29
It becomes highlight_green%28+37+%29%2Ax-481=0.
Look at highlight_red%28+37%2Ax-481+%29=0.
Solved linear equation highlight_red%28+37%2Ax-481=0+%29 equivalent to 37*x-481 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=13.

Universal Simplifier and Solver


Done!


As you can see from that huge box above,x=13
then number of $37 pcs=13
number of $22 pcs=(x-6)=7
then number of $48 pcs=35-(13+7)=35-20=15


Hence,he will have to order 15 of the $48 pcs


Prabhat.