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3 years ago

Lily bought 6 skirts and 5 coats for a total of $452.62. If Lily's

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

5 0

Let x = cost of one skirt

Let y = cost of one coat.

We need to construct a system of equations to help us solve this problem.

Lily: $452.62 = 6x + 5y

Sis: $289.36 = 3x + 5y.

Let's solve this by elimination. Multiply the second equation by -1

Lily: $452.62 = 6x + 5y

Sis: -$289.36 = -3x + -5y. Add the equations together.

$163.26 = 3x. Divide each side by 3.

$54.42 = x. Plug this into one of our original equations.

$452.62 = 6(54.42) + 5y. Multiply 6 by 54.42

$452.62 = 326.52 + 5y. Subtract 326.52 from each side.

$126.1 = 5y. Divide each side by 5

$25.22 = y.

One coat costs $25.22

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As a sales person Jonathan is paid 50 per week +3% of the total Amount he sells. This week he wants to earn at least 100. Write

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The Inequality with integer coefficient for the total sales is $5000+3x\geq 10000$

Hence Jonathan should make total sales of at least 1667 to earn at least 100.

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Addition amount = 3% of Total sales.

Let the Total sales be 'x'.

∴ Additional amount = $\frac{3}{100}x$

Amount he wants to earn this week $\geq$ 100

We need to write the inequality with integer coefficient for the total sales and also to find the total sales.

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We cans say that;

Amount paid per week plus Additional amount should be greater than or equal to Amount he wants to earn this week.

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$50+\frac{3}{100}x\geq 100$

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$\frac{50\times100}{100}+\frac{3}{100}x\geq 100$

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Multiplying both side by 100 we get;

$100 \times\frac{5000+3x}{100}\geq 100\times 100\\\\5000+3x\geq 10000$

Hence The Inequality with integer coefficient for the total sales is $5000+3x\geq 10000$

On solving the above equation we get;

Subtracting both side by 5000 we get;

$5000+3x-5000\geq 10000-5000\\\\3x\geq 5000$

Dividing both side by 3 we get;

$\frac{3x}{3}\geq \frac{5000}{3}\\\\x\geq 1666.67$

Hence Jonathan should make total sales of at least 1667 to earn at least 100.

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