One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced, wheras a second machine has a fixed daily cost of $10 and a variable cost of $2 per item produced. Using y to represent the total daily costs of these items, determine the number of items x for which the total daily costs will be the same. What is the total daily cost for this number of items? (Use substitution method and steps would be appreciated)
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substitution method word problem
- Thread starter LinkII08
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BigGlenntheHeavy
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\(\displaystyle Let \ f(x) \ = \ 50+\frac{3x}{2} \ and \ g(x) \ = \ 10+2x.\)
\(\displaystyle 50+\frac{3x}{2} \ = \ 10+2x, \ \implies \ x \ = \ 80.\)
\(\displaystyle Hence, \ f(80) \ = \ 50 \ +\frac{3}{2}(80) \ = \ 170, \ and\)
\(\displaystyle g(80) \ = \ 10+2(80) \ = \ 170.\)
\(\displaystyle 50+\frac{3x}{2} \ = \ 10+2x, \ \implies \ x \ = \ 80.\)
\(\displaystyle Hence, \ f(80) \ = \ 50 \ +\frac{3}{2}(80) \ = \ 170, \ and\)
\(\displaystyle g(80) \ = \ 10+2(80) \ = \ 170.\)