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Topic: **Help in solving a math problem****Question:**
I need help on these 2 problems. im 11 and in fifth grade.
1) A jeweler has 240 gemstones and 12 velvet boxes. if each box can contain up to 32 stones, what is the best way to use them if the jewler wants to use the fewest number of boxes?
2) What if he wants to find the fewest number of gems?

July 16, 2019 / By Pearlie

1- You can put 32 stones in 7 boxes and 16 in 1 box using a total of 8 boxes. 2- put 20 stones in 12 boxes. 240 / 12= 20 stones

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2/3 of 150 gallons is (2/3)*(150 = 100 gallons 1 cap of solution is required for each 20 gallons there are 5 (20 gallons) in 100 gallons: 100/20 = 5 For each of those 5 you need 1 cap You need 5 full caps of solution if the tank is 2/3 full. (150)(2/3)/20)*1 = 5 For future applications, simply divide the number of gallons by 20. That's the number of full caps you need to use. For example, if the tank is full with 150 gallons of water: 150/20 = 7.5 → 7 1/2 caps of solution

10 ml = 1 full cap of solution and 10 ml is required to clean every 20 gallons of water. The stock tank holds 150 gallons, but is currently only 2/3 the way full. 5 caps of solution is required to clean the current amount of water in the stock tank. I found what I need at Petco and most of the bottles say 5ml of solution for every 10 gallons. 5 ml is half a cap of the solution lid so I doubled that for fewer measuring instances and now my head is running in circles as I confuse myself on how many full caps to use.

1) A jeweler has 240 gemstones and 12 velvet boxes. if each box can contain up to 32 stones, what is the best way to use them if the jewler wants to use the fewest number of boxes? Divide 240 by 32 for the initial number of boxes. You will have a remainder, meaning one more box.

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G = 240 gemstones B = 12 velvet boxes Q = 32 stones/box Q = G/B B = G/Q B = 240/32 = 7 16/32 8 boxes total with one box containing only 16 gemstones 2) Q = G/B = 240/12 = 20 gemstones/box

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1. Explain the solution to the system Given system: 6x + 3y = 12 2x = 8 - y Rewrite the second one so it matches the pattern of the first. 2x = 8 - y 2x + y = 8 Your two systems are now: 6x + 3y = 12 2x + y = 8 Multiply the second equation by -3. -3(2x + y) = -3(8) -3(2x) - 3(y) = -24 -6x - 3y = -24 Your modified system is now: 6x + 3y = 12 -6x - 3y = -24 Add the two systems together. 6x + 3y = 12 -6x - 3y = -24 ------------------------ 0 ≠ -12 Both of the terms get eliminated. However, 0 is never equal to -12, so there is no solution. ANSWER: No solution 2. Find the equation in slope intercept form of a line that passes through (2, -5) and is perpendicular to y = (1 / 4)x + 7 Remember the slope-intercept form of a line equation is: y = mx + b m = slope b = y-intercept Given: y = (1 / 4)x + 7 Means: m_given = (1 / 4) Remember perpendicular lines have a slope that is a negative inverse of the other. m_perpendicular = -1 / m_given Plug in the given slope to find the perpendicular slope. m_perpendicular = -1 / (1 / 4) = -1 * (4 / 1) = -1 * 4 = -4 Plug this into the the general equation. y = mx + b y = -4x + b Given: point (2, -5) Means: x = 2, y = -5 Use these values to find b by plugging them into the equation you have so far. y = -4x + b -5 = -4(2) + b -5 = -8 + b -5 + 8 = -8 + b + 8 3 = b Update your equation with the found b value. y = -4x + b y = -4x + 3 ' ANSWER: y = -4x + 3

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