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

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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

Bytelearn · Accepted Answer

Determine ratio calculation: Determine the ratio of green to silver beads used per 5cm of the belt. Aspen uses 40 green beads and 24 silver beads for every 5cm of the belt. Ratio of green to silver beads = 40/24 = 5/3Initial ratio calculation: Calculate the initial ratio of green to silver beads Aspen has. Aspen has 306 green beads and 210 silver beads. Initial ratio of green to silver beads = 306/210 = 1.4571 (approximately)Segments calculation: Find the number of 5cm segments Aspen can sew before the ratio of green to silver beads changes. Since the initial ratio of green to silver beads is higher than the ratio of beads used per 5cm, Aspen will run out of silver beads before green beads. We need to find the point at which the remaining green and silver beads are in the same ratio as the beads used per 5cm segment. Let x be the number of 5cm segments sewn when the ratio becomes equal. Remaining green beads = 306 - 40x Remaining silver beads = 210 - 24x We want the remaining beads to have the same ratio as the beads used per segment: (306 - 40x) / (210 - 24x) = 5/3Equation solving: Solve the equation to find the value of x. Cross-multiply to solve for x: 3(306 - 40x) = 5(210 - 24x) 918 - 120x = 1050 - 120x Since the x terms cancel each other out, this indicates that there is no solution to the equation, which means there is a math error in the previous steps.

Aspen has $306$ green beads and $210$ silver beads. For every $5\text{cm}$ 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? $\text{cm}$

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Aspen has 306306306 green beads and 210210210 silver beads. For every 5cm5\text{cm}5cm of a belt that Aspen sews, they use 404040 green beads and 242424 silver beads. After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?cm\text{cm}cm

Aspen has $306$ green beads and $210$ silver beads. For every $5\text{cm}$ 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? $\text{cm}$