# 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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