Math Problem Monday - October 1st, 2018 | Mathnasium Livermore, CA

Oct 1, 2018 | Livermore

Lower Elementary
Question: Randy had 8 pens but lost 4. If he found 7 more, how many pens did he have?
Answer: 11 pens
Note: Randy started out with 8 pens but lost 4
8 pens – 4 pens = 4 pens
Then he found 7 more pens.
4 pens + 7 pens = 11 pens

Upper Elementary
Question: Linda has ¾ of her birthday cake left over and she wants to share it with 11 of her friends. How much of the cake would everyone get if each person received an equal sized piece?
Answer: 1/16
Note: Because Linda only had ¾ of her cake, we need to brake ¾ of the cake in to 12 pieces (Linda + her 11 friends). Because we have ¾ of the cake, each ¼ needs to be broken into 4 pieces creating 12 pieces. If Linda had the whole cake and she broke each ¼ into 4 pieces, there would be 16 pieces. So everyone gets 1/16 of the cake.

Middle School
Question: In 16 years Benjamin will be three times as old as he is now. How old is he now?
Answer: 8 years old
Note: We start by writing this problem algebraically. If Benjamin is x years old then in 16 years he will be 3x. So,
x + 16 = 3x
“if we take his age now and add 26 years it will equal to 3 times his age now.”
Solving for x,
2x = 16
x = 8

Algebra and Up
Question: Lucy wants to make a 100-pound mixture of almonds and cashew that she will sell for $8.50 per pound. Lucy can buy almonds for $7.79 per pound and cashews for $4.99 a pound. If she wants to yield a 60% profit, how many pounds of each type of nut does Lucy use for her mixture? (Round answers to the nearest tenth.)
Answer: About 11.4 pounds of almonds and 88.6 pounds of cashews
Note: This problem has two unknowns, so in order to solve for the two unknowns we will need two equations. Let a equal the amount in pounds for almonds and let c equal the amount in pounds for cashews.
a + c = 100 (1)
Because she wants to yield a 60% profit she needs to make sure that her mixture 160% of the cost of her mixture equals $8.50. Let x equal the cost she pays for a pound of the mixture.
1.6x = 8.50
x = 8.50/1.6 ≈ 5.31
Now that we know how much Lucy’s mixture cost per pound we can use it in our second equation.
a(7.79) + c(4.99) = 100(5.31) (2)
Recalling equation 1 and solving for c, we can then plug it into equation 2.
c = 100 – a
a(7.79) + (100 – a )(4.99) = 100(5.31)
Solve for a.
a(7.79) + 499 – a(4.99) = 531
2.80a = 32
a = 11.4 pounds
Now we solve for c using equation 1.
11.4 + c = 100
c = 88.6 pounds

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