Amanda is placing an order for running shoes and leather boots for her footwear boutique. She needs a total of 48 pairs of shoes and twice as many pairs of running shoes as leather boots.

Set up the two equations that can be used to find the number of each type of shoe that Amanda needs to order.

Let the equation that represents the total number of pairs of shoes be referred to as constraint 1.
Let constraint 2 refer to the equation that describes the ratio of the number of running shoes to leather boots.

Only constraint _ would be met if 18 pairs of leather boots and 36 pairs of running
shoes were ordered.

Only constraint _ would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

Question

25-06-2019
Mathematics

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Amanda is placing an order for running shoes and leather boots for her footwear boutique. She needs a total of 48 pairs of shoes and twice as many pairs of running shoes as leather boots.

Set up the two equations that can be used to find the number of each type of shoe that Amanda needs to order.

Let the equation that represents the total number of pairs of shoes be referred to as constraint 1.
Let constraint 2 refer to the equation that describes the ratio of the number of running shoes to leather boots.

Only constraint _ would be met if 18 pairs of leather boots and 36 pairs of running
shoes were ordered.

Only constraint _ would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

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jdoe0001 jdoe0001 · Answer 1 · 2019-06-26T00:14:27+02:00

b = amount of leather boots

r = amount of running shoes

she needs a total of 48 altogether, so then b + r = 48. <--- constraint 1

however, she also needs twice as many "r" as she needs "b", so, whatever "r" amount is, we know is twice "b", namely r = 2b. <--- constraint 2.

now, if b = 18 and r = 36, well, 36 is twice as much as 18, so constraint 2 is met, but but but, 18 + 36 = 54, constraint 1 is not.

well, if b = 12 and r = 36, well, 12 + 36 = 48, so constraint 1 is met, but but but, 36 is not twice as much as 12, is actually three times as much, so constraint 2 is not.

anthougo anthougo · Answer 2 · 2021-11-04T23:07:34+01:00

1. Only constraint 2 would be met if 18 pairs of leather boots and 36 pairs of running shoes were ordered.

Constraint 2 is satisfied because 18 pairs of leather boots equals 1/2 of the running shoes.

2. Only constraint 1 would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

Constraint 1 is satisfied because 12 pairs of leather boots 36 pairs of the running shoes equal 48 pairs (12 + 36).

Data and Calculations:

Total pairs of shoes required = 48 pairs

Running shoes required (r) = 2 of leather boots

Leather boots required (b)= 1/2 of running shoes

Constraint 1:

The total pairs of different shoes required:

Running shoes = 32r

Leather boots = 16b

Total pairs = 32r + 16b = 48

Constraint 2:

Ratio equation:

Running shoes = 2r

Leather boots = b

Equation = 2r + b = 48

Thus, Constraint 2 satisfies the first order, while Constraint 1 satisfies the second order. The two constraints do not satisfy the two orders.

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