Question

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

Answer 1

$24

Explanation:

Let
`b` = bowl

Let
`p` = plate

Given:

• 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,
`b=p`, totaling to $96.

`b=p\\2p + 6b = 96`

2) We can solve for
`p` these two equations simultaneously using the substitution ot elimination method. I will demonstrate using the substitution method here.

`2p + 6(p) = 96\\2p+ 6p = 96\\8p = 96\\p = (96)/(8) \\p = 12`

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.

`1p` = $2

`12p` = $24

Answer 2

$24

Explanation:

Cost per plate: $2

Cost per Bowl: $2 + $4 = $6

Cost of 1 Plate and 1 Bowl: $2 + $6 = $8

Total cost of $96 divided by Cost of 1 Plate and 1 Bowl $8 = 12 sets of 1 Plate and 1 Bowl

12 plates x $2 Cost per Plate = $24