A phrase such as
"The number of red beads used is more than twice the number of yellow beads by 10"
seems to cause a lot of difficulty, since students often get confused where to add or subtract the difference given.
Perhaps this will help:
state the given as an inequality,
r > 2y by 10
now "balance" that inequation, that is, add 10 to the lesser side:
r = 2y + 10
similarly :
"the number of green beads used is more than one-third the number of yellow beads by 7"
g > (1/3)y by 7 ----> g = (1/3)y + 7
3g = y + 21
so 2y + r + 6g = 160
2y + (2y+10) + 2(3g) = 160
2y + 2y + 10 + 2y + 42 = 160
6y = 108
y = 18
so she uses 18 yellows
r = 2(18) + 10 = 46
3g = 18+21 = 39
g=13
she uses 18 yellows, 46 reds, and 13 greens
What is your conclusion for b) ?
Check my answer to make sure all conditions are met.
remember we are talking about the number of beads and the weight of the beads.
Nicole makes a keychain by using yellow, red and green beads. The number of red beads used is more than twice the number of yellow beads by 10, while the number of green beads used is more than one-third the number of yellow beads by 7. It is known that each yellow bead, red bead and green bead weigh 2 g, 1 g and 6 g respectively. The total weight of the beads used is 160 g.
a) Find the number of yellow beads used.
b) Nicole claims that she makes the keychain with not more than 80 beads. Do you agree? Explain your answer.
2 answers
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