Respuesta :
Answer: (a) The ratio of spirit to varnish is 1 : 3
(b) You will need 80 ml of mineral spirits
(c) Ratio = 3 : 2
Step-by-step explanation: (a) If you have to mix 25% mineral spirit to the varnish as required in the question, then the whole solution would effectively contain 25 percent spirit and 75 percent varnish, giving you a hundred percent solution. To express both quantities in ratio can be done as follows;
Ratio = Spirit : Varnish
Ratio = 25 : 75
Ratio = 1 : 3
(b) Next, if you use 240 ml of varnish, this quantity would constitute 75 percent or ratio 3 out of 4 of your total solution. Therefore 240 ml of varnish can be expressed as follows;
240 : x = 3 : 4
Where x is the total solution and the right hand side (3 : 4) expresses the ratio of varnish in relation to the total solution. Hence,
240/x = 3/4
By cross multiplication you now have,
3x = 240 * 4
x = 960/3
x = 320
If x is the total solution which is 320 ml, and varnish constitutes 240 ml, then spirit equals,
Spirit = Total solution - varnish
Spirit = 320 - 240
Spirit = 80.
Therefore, you would need 80 ml of mineral spirits.
(c) Robson's tapestries all measure 1.5 m by 1 m. This can be expressed in whole numbers by first eliminating the decimal. Multiplying both dimensions by 10 results in,
1.5 (10) x 1 (10)
15 x 10
If both measurements can also be expressed as 15 m by 10 m, then reducing to the least terms would result in 3 by 2. That is,
15/5 by 10/5
3 by 2
Expressed as a ratio, this now becomes
Ratio = 3 : 2
The ratio of spirit to varnish is 1:3, the quantity of mineral spirits required is 80 ml and the proportion of the height of tapestries to the width is 3:2.
What is percentage ?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
- 1-The ratio of spirit to varnish-
It need to mix 25% mineral spirits to the varnish. For this the solution must contain the 25% mineral spirits and 75% of varnish.
The ratio of spirit to varnish become,
[tex]r=\dfrac{25}{75}\\r=\dfrac{1}{3}[/tex]
- 2-The quantity of mineral spirits required-
Total 240 ml of varnish is there, which is equal to the 75% of the varnish. Let x is the total amount of solution. Thus,
[tex]x=\dfrac{240}{75}\times100\\x=320[/tex]
Now the there are total 25% of mineral spirits in the solution of 320 ml. Thus, the 25% of 320 ml is,
[tex]\rm Mineral \;Spirits=\dfrac{320}{100}\times25\\\rm Mineral \;Spirits=80\; ml[/tex]
- 3-Robison's tapestries all measure 1.5m x 1m wide.
Let L is the length and W is the width. Then the length and width in whole number can be express as,
[tex]L=15\rm \;,m\\W=10\; m[/tex]
The ratio of length to width is,
[tex]\dfrac{L}{W}=\dfrac{15}{10}\\\dfrac{L}{W}=\dfrac{3}{2}[/tex]
Thus, the ratio of spirit to varnish is 1:3, the quantity of mineral spirits required is 80 ml and the proportion of the height of tapestries to the width is 3:2.
Learn more about the percentage here;
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