Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Aspen has 306 green beads and 210 silver beads. For every 5cm of a belt that Aspen sews, they use 40 green beads and 24 silver beads. After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left? ◻cm

Aspen has 306306 green beads and 210210 silver beads. For every 5 cm5\,\text{cm} of a belt that Aspen sews, they use 4040 green beads and 2424 silver beads.\newline After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?\newline□\squarecm\text{cm}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Pythagorean Theorem and its converseright chevron icon

Full solution

Q. Aspen has 306306 green beads and 210210 silver beads. For every 5 cm5\,\text{cm} of a belt that Aspen sews, they use 4040 green beads and 2424 silver beads.\newline After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?\newline□\squarecm\text{cm}
  1. Calculate ratio: Calculate the ratio of green to silver beads used per 5 cm5\,\text{cm} of belt.\newlineGreen to silver ratio = 4040 green beads : 2424 silver beads.
  2. Simplify ratio: Simplify the ratio to find the smallest whole number ratio.\newline408=5\frac{40}{8} = 5 green beads and 248=3\frac{24}{8} = 3 silver beads.\newlineSo, the simplified ratio is 55 green beads : 33 silver beads.
  3. Find sets needed: Find out how many sets of beads Aspen can use before running out.\newlineGreen bead sets = 3065=61.2\frac{306}{5} = 61.2 sets.\newlineSilver bead sets = 2103=70\frac{210}{3} = 70 sets.
  4. Calculate green beads: Since Aspen can't use a fraction of a set, they can use only 6161 full sets of green beads.
  5. Calculate silver beads: Calculate the number of silver beads used after 6161 sets.\newlineSilver beads used = 6161 sets ×3\times 3 silver beads/set = 183183 silver beads.
  6. Calculate silver beads left: Calculate the number of silver beads left after using 6161 sets.\newlineSilver beads left =210−183=27= 210 - 183 = 27 beads.
  7. Calculate green beads left: Calculate the number of green beads left after using 6161 sets.\newlineGreen beads left = 306−(61 sets×5 green beads/set)=306−305=1306 - (61 \text{ sets} \times 5 \text{ green beads/set}) = 306 - 305 = 1 bead.

More problems from Pythagorean Theorem and its converse

Question
Find all solutions with 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecos⁡(θ)=−1\cos(\theta) = -1\newline‾∘\underline{\hspace{2em}}^\circ
Get tutor helpright-arrow

Posted 2 months ago

Question
Kimi's school is 1515 kilometers west of her house and 88 kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?\newline_____\_\_\_\_\_ kilometers
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.\newlinecos⁡35∘=\cos 35^\circ = __
Get tutor helpright-arrow

Posted 2 months ago

Question
Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
The terminal side of an angle θ\theta in standard position intersects the unit circle at (8485,1385)(\frac{84}{85}, \frac{13}{85}). What is cos⁡(θ)\cos(\theta)?\newlineWrite your answer in simplified, rationalized form.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecsc⁡60∘=\csc 60^\circ = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecos⁡90∘=\cos 90^\circ = ____
Get tutor helpright-arrow

Posted 3 months ago

View all (129)