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Systems of Equations Application Word Problems and Systems of Inequalities (8 Problems)

# 41 Nickels and dimes. Windborne has 35 coins consisting of dimes and nickels. If the value of his coins is # 3.30, then how many of each type does he have?

# 43 Blending fudges. The chocolate factory in Vancouver blends its double-dark-chocolate fudge, which is 35% fat, with its peanut butter fudge, which is 25% fat, to obtain double-dark-peanut fudge, which is 29% fat.

A) Use a graph to estimate the number of pounds of each type that must be mixed to obtain 50 pounds of double-dark-peanut fudge.
B) Write a system of equations and solve it algebraically to find the exact amount of each type that should be used to obtain 50 pounds of double-dark-peanut fudge.

# 18 2 x + y < 3
X -- 2y > 2

#25 y > 2x -- 4
Y < 2x + 1

# 28 y < x
Y < 1

# 34 3 xs + 2y < 2
--x -- 2y > 4

#38 y > x
Y < -- x

#39 x + y < 5
x -- Y > -- 1

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# 41 Nickels and dimes. Windborne has 35 coins consisting of dimes and nickels. If the value of his coins is # 3.30, then how many of each type dose he have?

Solution:

Let x be the number of nickels and y be the number of dimes.
Then x + y = 35.-------(1)
The value of his coins is $330 = 330 cents.
So number of coins*its value gives the total value.
So 5x + 10 y = 330. -------(2).

Multiply the first equation by -5
-5x - 5y = -175.
5x + 10 y = 330.
---------------------. Add both equations. We get,
0 + 5y = 155
y = 31

Plug in this value in the first equation.
X + 31 = 35.
X = 35- 31
X = 4.
Therefore the number of nickels = 4, number of dimes = 31.

# 43 ...

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Systems of Equations Application Word Problems and Systems of Inequalities are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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