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Elodia [21]
3 years ago
6

The price of a toy costing £50 is increased to £65 work out the percentage increase

Mathematics
1 answer:
lions [1.4K]3 years ago
8 0

Answer:

Percent increase = 30%

Step-by-step explanation:

Given that:

Old price of toy = £50

New price of toy = £65

Difference = New price - Old price

Difference = 65 - 50

Difference = £15

Percent increase = \frac{Difference}{Old\ price}*100

Percent increase = \frac{15}{50}*100

Percent increase = 0.3 * 100

Percent increase = 30%

Hence,

Percent increase = 30%

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y = gallons of the 2% butterfat milk


now, we'll be adding "x" gallons of the 7% one, but we know that, is really "x" gallons, but only 7% of it is butterfat, the rest is water and other subtances.

so, in "x" gallons, how many gallons is butterfat only anyway?  namely, what is 7% of "x"?  well, (7/100) * x, or 0.07x.

likewise, how many gallons of butterfat are in the 2% one?  well, (2/100) * "y" or 0.02y.

we know that, whatever "x" and "y" add up to 275 gallons, thus x + y = 275.

we also know that, the butterfat amounts add up to the same butterfat in the 275 gallons, thus

\bf \begin{array}{lccclll}&#10;&\stackrel{gallons}{amount}&\stackrel{butterfat~\%}{quantity}&\stackrel{butterfat~gallons}{quantity}\\&#10;&------&------&------\\&#10;\textit{7\% butterfat milk}&x&0.07&0.07x\\&#10;\textit{2\% butterfat milk}&y&0.02&0.02y\\&#10;--------&------&------&------\\&#10;mixture&275&0.05&13.75&#10;\end{array}

\bf \begin{cases}&#10;x+y=275\implies \boxed{y}=275-x\\&#10;0.07x+0.02y=13.75\\&#10;----------\\&#10;0.07x+0.02\left( \boxed{275-x} \right)=13.75&#10;\end{cases}&#10;\\\\\\&#10;0.07x-0.02x+5.50=13.75\implies 0.05x=8.25&#10;\\\\\\&#10;x=\cfrac{8.25}{0.05}\implies x=165

how much will it be of the 2% milk?  well, y = 275 - x.
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