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34 votes
34 votes
4. Tyler filled a small jar with quarters and dimes and donated it to his school'scharity club. The club member receiving the jar asked, "Do you happen toknow how much is in the jar?" Tyler said, "I know it's at least $8.50, but I don'tknow the exact amount."4a. Write an inequality to represent the relationship between the numberof dimes, d, the number of quarters, q, and the dollar amount of the moneyin the jar.

User Xhh
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1 Answer

17 votes
17 votes

Let

y -----> number of quarters

x ----> number of dimes

we have that

the inequality that represents this situation is

Remember that

1 quarter =$0.25

1 dime=$0.10

so


0.25y+0.10x\ge8.50

rewrite the variables


0.25q+0.10d\ge8.50

see the attached figure to better understand the problem

Part 4b

The solution of the given inequality is the shaded area above the solid line 0.25q+0.10d=8.50

A solution to this inequality could be the point (50,50)

that means

the number of quarters is 50 and the number of dimes is 50

the ordered pair must satisfy the inequality

Verify


\begin{gathered} 0.25q+0.10d\ge8.50 \\ 0.25(50)+0.10(50)\ge8.50 \\ 12.50+5\text{ }\ge8.50 \\ 17.50\text{ }\ge8.50\text{ --}\longrightarrow\text{ is ok} \end{gathered}

Part 4c

we have that

d=25 dimes

substitute in the inequality and solve for q

so


0.25q+0.10(25)\ge8.50

solve for q


\begin{gathered} 0.25q+2.5\ge8.50 \\ 0.25q\ge8.50-2.5 \\ 0.25q\ge6 \\ q\ge24 \end{gathered}

the number of quarters must be greater than or equal to 24

4. Tyler filled a small jar with quarters and dimes and donated it to his school'scharity-example-1
User Lxvs
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