math
Maggie has a box of 300 colored blocks.The box has a equal number of green and blue blocks and an equal number of red and yellow blocks.If Maggie arranged all of the green blocks in stacks of 10 and all of the blue blocks in stacks of 7,how many yellow blocks are in the box?
asked by
xavier

clearly, if there are x stacks of green & blue, and y of red & yellow, then
20x+14y = 300
10x+7y = 150
y = (15010x)/7
y = 10(15x)/7
Since there must be an integer number of blocks, and 7 does not divide 10, it must divide 15x
So, 15x = 7 or 14
and y = 10 or 20
So, there may be 70 yellow and red, and 80 green & blue
or 140 yellow and red, and 10 green & blueposted by Steve

70
posted by richard
Respond to this Question
Similar Questions

math
A maker of cubic number blocks packs a rectangular box so that there are 11 blocks along one edge, 8 blocks along the second edge and 2 blocks along the third edge. How many blocks will be shipped in this box. If each block has a 
Math
A maker of a cubic number blocks packs a rectangular box so that there are 8 blocks along one edge, 10 blocks along the second edge, and 4 blocks along the third edge. How many blocks will be shipped in this box 
Math
The kindergarten has a box of blocks.Some blocks are red,some yellow and some are blue.1/2 of the blocks are red,1/4 of the blocks are yellow and 24 of the blocks are blue.How many blocks are in the box? 
Math
Heather has a bag with 16 red blocks, 11 blue blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she was to draw a block out of the bag, record the color and replace the block back in the bag, 
Math
Heather has a bag with 16 red blocks, 11 blue blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she was to draw a block out of the bag, record the color and replace the block back in the bag, 
Math
Heather has a bag with 16 red blocks, 11 blue blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she was to draw a block out of the bag, record the color and replace the block back in the bag, 
Math
1) Which sum best represents the model shown below? There are 3 blue blocks, and each of them separately equal x^2. There are 2 green blocks that each separately equal x. There are 2 red blocks that each separately equal 1. And 
math
manfred mouse fell inside a box of toy blocks. to escape, he needs to build a stairway with the blocks. for manfred to escape, the stairway must be 8 blocks high. he starts with 8 blocks for the bottom step. for the next step, he 
Pittsburgh public school
There are a total of 10 blocks in the blocks. Bassein the results of Emily 20 draws, how many yellow, green, red and blue blocks would you expet to be in the bucket? Explain 
Math
Many has two boxes one contains 10 colored pencils 4 of witch are red and 6 which are green the other box onther box contains 7 markers and which 4 are red and 3 are blue what's the probability of of many choosing green green