Chapter 3.6, Problem 38PPSE

Solution

i.

To identify: How the equations shown below relates to the problem and what does each variable represents? Also, it is given that fill nine 1-lb tins with a snack mix. You have $15 and buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $0.85 per lb. The mixture contains an equal number of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

  $\left\{\begin{array}{l}x+y+z=9\\ 2.45x+1.85y+0.8z=15\\ x+y=2z\end{array}\right.$

x is the quantity of almonds required, y is the quantity of hazelnuts and z is the quantity of raisins required.

The equation $x+y+z=9$ represents the nine 1-lb tines with a snack mix.

The equation $2.45x+1.85y+0.8z=15$ represents the number of almonds hazelnuts and raisins buy in $15.

The equation $x+y=2z$ represents the quantity of almonds hazelnuts and raisins.

Given information:

It is given that fill nine 1-lb tins with a snack mix. You have $15 and buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $0.85 per lb. The mixture contains an equal number of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

Explanation:

Consider the given information.

Let x is the quantity of almonds required, y is the quantity of hazelnuts and z is the quantity of raisins required.

It is given that fill nine 1-lb tins with a snack mix.

Thus, $x+y+z=9$

Also, spent $15 to buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $0.85 per lb.

This can be written as: $2.45x+1.85y+0.8z=15$

The mixture contains an equal number of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

This can be written as: $x+y=2z$ .

ii.

To calculate: The value of unknown variable if it is given that fill nine 1-lb tins with a snack mix. You have $15 and buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $0.85 per lb. The mixture contains an equal number of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

  $\left\{\begin{array}{l}x+y+z=9\\ 2.45x+1.85y+0.8z=15\\ x+y=2z\end{array}\right.$

The required value is $x=2.5,y=3.5,\text{ and }z=3$ .

Given information:

It is given that fill nine 1-lb tins with a snack mix. You have $15 and buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $0.85 per lb. The mixture contains an equal number of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

Explanation:

Consider the given information.

From the given information the system of equations is:

  $\left\{\begin{array}{l}x+y+z=9\\ 2.45x+1.85y+0.8z=15\\ x+y=2z\end{array}\right.$

Write it into matrix form.

  $\left[\begin{array}{cccc}1& 1& 1& 9\\ 2.45& 1.85& 0.8& 15\\ 1& 1& -2& 0\end{array}\right]$

Now use Calculator to solve the equation.

Step 1: Press the 2ND key then press MATRX and select EDIT.

Step 2: Click 1 to access matrix A.

Step 3: Input the dimensions and enter the entries by pressing ENTER after each value.

  

Step 4: Press 2ND QUIT 2ND MATRX and select MATH.

Step 5: Click ALPHA B 2ND MATRX 1 ) .

  

Step 6: Now press ENTER.

  

The required value is $x=2.5,y=3.5,\text{ and }z=3$ .

iii.

To identify: How each ingredient should buy if $x=2.5,y=3.5,\text{ and }z=3$ .

Buy 2.5 lb of almonds, 3.5 lb of hazelnuts and 3 lb of raisin.

Given information:

The value of $x=2.5,y=3.5,\text{ and }z=3$ and the given system of equation is:

  $\left\{\begin{array}{l}x+y+z=9\\ 2.45x+1.85y+0.8z=15\\ x+y=2z\end{array}\right.$

Explanation:

Consider the given information.

From part (a) it is known that x is the quantity of almonds required, y is the quantity of hazelnuts and z is the quantity of raisins required.

From the part(b) it is known that $x=2.5,y=3.5,\text{ and }z=3$ .

Thus, Buy 2.5 lb of almonds, 3.5 lb of hazelnuts and 3 lb of raisin to make nine-1lb tins with a snack mix.