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
. Since