Math

QuestionColleen uses blue yarn bb and red yarn rr. What equation shows their proportional relationship? Options: (A) b=25rb=\frac{2}{5} r, (B) r=25br=\frac{2}{5} b, (C) b=27rb=\frac{2}{7} r, (D) r=27br=\frac{2}{7} b.

Studdy Solution

STEP 1

Assumptions1. For every45 pieces of blue yarn,18 pieces of red yarn are used. . The relationship between the amount of blue yarn, bb, and red yarn, rr, is proportional.

STEP 2

We need to find the ratio of blue yarn to red yarn. This can be calculated by dividing the number of blue yarn pieces by the number of red yarn pieces.
Ratio=BlueyarnRedyarnRatio = \frac{Blue\, yarn}{Red\, yarn}

STEP 3

Now, plug in the given values for the number of blue yarn pieces and red yarn pieces to calculate the ratio.
Ratio=4518Ratio = \frac{45}{18}

STEP 4

implify the fraction to get the ratio in its simplest form.
Ratio=4518=2Ratio = \frac{45}{18} = \frac{}{2}

STEP 5

The ratio 52\frac{5}{2} means that for every5 pieces of blue yarn,2 pieces of red yarn are used. This can be represented as an equation where bb represents the amount of blue yarn and rr represents the amount of red yarn.
b=52rb = \frac{5}{2} r

STEP 6

However, the options provided in the problem are in the form of 25\frac{2}{5} and 2\frac{2}{}, not 52\frac{5}{2}. Therefore, we need to take the reciprocal of our ratio to match the form of the options.
Reciprocalofratio=25Reciprocal\, of\, ratio = \frac{2}{5}

STEP 7

Substitute this reciprocal ratio into the equation where rr represents the amount of red yarn and bb represents the amount of blue yarn.
r=25br = \frac{2}{5} bThis equation represents the proportional relationship between the amount of blue yarn and red yarn that Colleen uses when knitting a scarf.
The correct answer is (B) r=25br=\frac{2}{5} b.

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