An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 sm

all baskets and 4 large baskets, using a total of 60 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 10 large baskets, using a total of 132 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include______pieces and the large ones each include_____pieces.

Mathematics

1 answer:

Bingel [31]4 years ago

5 0

$Let \: x, y \: (x,y>0) \: be \: the \: number \: of \: fruits \: the \: small \: and \: large \: baskets \: hold \: respectively \\ We \: have \: a \: system \: of \: equations:2x + 4y = 60 \: \wedge \: 2x + 10y = 132 \\ \Leftrightarrow x = 6 \: \wedge \: y = 12 \\ \Rightarrow The \: small \: baskets \: each \: include \: 6 \: fruits \\ \Rightarrow The \: large \: baskets \: each \: include \: 12 \: fruits$

You might be interested in

Find the slope and y intercept of the graph of the graph of each equation.

AleksandrR [38]

Solve each equation for y and then the slope is m and y-intercept is b as in:
$y = mx+b$

So, if you do that, you'll get (remember, this is <em>after</em> solving for y):
1. m = -6, b = -2
2. m = 5, b = -1
3. m = -5/3, b = 5
4. m = 0, b = -1/4
5. m = -1, b = -3
6. m = 3, b = -4
7. m = 1/2, b = -5/2
8. m = 7/2, b = 1

Hope this helps.

7 0

4 years ago

Read 2 more answers

In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: The length of the angle bisector of a

Aliun [14]

Check the picture below.

$\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\quad cos(CAB)=\cfrac{5}{13}\implies \measuredangle CAB=cos^{-1}\left( \frac{5}{13} \right)
\\\\\\
\textit{that means that }\measuredangle hAC=\cfrac{cos^{-1}\left( \frac{5}{13} \right)}{2}\impliedby \textit{one of the halves}$

now, notice, for the angle hAC, the hypotenuse is hA, and the adjacent side is CA, therefore,

$\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(hAC)=\cfrac{5}{hA}\implies hA=\cfrac{5}{cos(hAC)}
\\\\\\
hA=\cfrac{5}{cos\left[ \frac{cos^{-1}\left( \frac{5}{13} \right)}{2} \right]}$

make sure your calculator is in Degree mode, if you need the angle in degrees.