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QuestionMonica knits 10 inches/day after 16 inches; Sean knits 14 inches/day. Find dd for equal lengths: 16+10d=14d16 + 10d = 14d. How many days?

Studdy Solution

STEP 1

Assumptions1. Monica has already knitted16 inches of her scarf. . Monica knits10 inches of her scarf each day.
3. Sean is just starting his scarf.
4. Sean knits14 inches of his scarf each day.
5. We want to find the number of days it will take for Sean's scarf to be the same length as Monica's.

STEP 2

We can set up an equation to represent the lengths of the scarves after dd days.For Monica, she has already knitted16 inches and will knit an additional10 inches each day, so after dd days, the length of her scarf is 16+10d16 +10d inches.
For Sean, he is just starting his scarf and will knit14 inches each day, so after dd days, the length of his scarf is 14d14d inches.
We want to find the number of days dd it will take for Sean's scarf to be the same length as Monica's, so we can set up the following equation16+10d=14d16 +10d =14d

STEP 3

We can solve this equation for dd by subtracting 10d10d from both sides of the equation.
16+10d−10d=14d−10d16 +10d -10d =14d -10d

STEP 4

implify the equation.
16=4d16 =4d

STEP 5

Finally, we can solve for dd by dividing both sides of the equation by4.
d=164d = \frac{16}{4}

STEP 6

Calculate the value of dd.
d=164=4d = \frac{16}{4} =4It will take4 days for Sean's scarf to be the same length as Monica's.

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