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2 years ago

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Mathematics

1 answer:

pishuonlain [190]2 years ago

5 0

Answer:

Cost of small box of oranges = 7

Cost of small box of oranges = 13

Step-by-step explanation:

Step 1) Let the cost of small box of oranges = x

Let the cost of small box of oranges = y

Step 2)

Equation 1) Matt sells 3 small boxes and 14 large boxes for Php. 203

3x + 14y = 203 -------------------(I)

Equation 2) Ming sells 11 small boxes and 11 large boxes for Php. 220

11x + 11y = 220 ----------------(II)

Step 3:

Multiply equation (I) by 11 and equation (II) by (-3).

(I)*11 33x + 154y = 2233

(II)*(-3) <u>-33x - 33y = -660 </u> {Now add and x will be eliminated}

121y = 1573

y = 1573/121

y = 13

Substitute y = 13 in equation (II)

11x + 11*13 = 220

11x + 143 = 220

11x = 220 - 143

11x = 77

x = 77/11

x = 7

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3 years ago

The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

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Answer:

2 $\frac{1}{16}$

Step-by-step explanation:

The question state that; the sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

First, we need to interpret and represent this statement mathematically

Let n be the number.

The sum means 'addition'

1/6 of that number is 1/6 of n = 1/6 × n = $\frac{n}{6}$

2 1/2 of that number is 2 1/2 of n = 2 1/2 × n = 5/2 × n = $\frac{5n}{2}$

So the question says that, when we add; $\frac{n}{6}$ , $\frac{5n}{2}$ and 7 all together, the value is 12 1/2

That is;

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = 12 1/2

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$ ( changing 12 1/2 to improper fraction will give $\frac{25}{2}$ )

So we can now go ahead and solve for n

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$

subtract 7 from both-side of the equation

$\frac{n}{6}$ + $\frac{5n}{2}$ = $\frac{25}{2}$ - 7

$\frac{n + 15n}{6}$ = $\frac{25 -14}{2}$

$\frac{16n}{6}$ = $\frac{11}{2}$

$\frac{16n}{6}$ can be reduced to give us $\frac{8n}{3}$

$\frac{8n}{3}$ = $\frac{11}{2}$

Cross multiply

8n × 2 = 11× 3

16n = 33

Divide both-side of the equation by 16

$\frac{16n}{16}$ = $\frac{33}{16}$

(On the left-hand side of the equation, 16 will cancel-out 16 leaving us with just, while on the right-hand side of the equation 33 will be divided by 16)

n = $\frac{33}{16}$ = $2\frac{1}{16}$