rachel bought an equal number of bowls and plates for$96. each plate cost $2 and each bowl cost $4 more than each plate. how much did she spend on all the plates
Question
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Answer:$24Step-by-step explanation:Let [tex]b[/tex] = bowlLet [tex]p[/tex] = plateGiven:
- Equal number of bowls and plates for $96
- 1 plate = $2
- 1 bowl = $4 + $2 = $6
1) We can translate these into algebra. Since Rachel has equal number of bowls and plates, [tex]b=p[/tex], totaling to $96.[tex]b=p\\2p + 6b = 96[/tex]2) We can solve for [tex]p[/tex] these two equations simultaneously using the substitution ot elimination method. I will demonstrate using the substitution method here.[tex]2p + 6(p) = 96\\2p+ 6p = 96\\8p = 96\\p = \frac{96}{8} \\p = 12[/tex]So, Rachel bought 12 plates and 12 bowls since plates are equivalent to bowls.3) Use ratio to find the the cost of the plates.[tex]1p[/tex] = $2[tex]12p[/tex] = $24 -
Answer:$24Step-by-step explanation:Cost per plate: $2Cost per Bowl: $2 + $4 = $6Cost of 1 Plate and 1 Bowl: $2 + $6 = $8Total cost of $96 divided by Cost of 1 Plate and 1 Bowl $8 = 12 sets of 1 Plate and 1 Bowl12 plates x $2 Cost per Plate = $24