Answer: He bought 22 of one type and 13 of the other type of donut.
Step-by-step explanation: Since the question stated that he bought two types of donuts, we would call the donuts type a and type b. If he bought a variety of 35 donuts, then we can express this as;
a + b = 35
Also, if one type cost $2.35 and another type cost $1.75 and the total cost was $69.05, this we can also express as,
2.35a + 1.75b = 69.05
We now have a pair of simultaneous equations as follows;
a + b = 35 ———(1)
2.35a + 1.75b =69.05 ———(2)
From equation (1), we make a the subject of the equation, a = 35 - b
Substitute for the value of a into equation (2)
2.35(35 - b) + 1.75b = 69.05
82.25 - 2.35b + 1.75b = 69.05
Collect like terms and we have
83.25 - 69.05 = 2.35b - 1.75b
13.2 = 0.6b
Divide both sides of the equation by 0.6
22 = b
With the value of b now known, substitute for the value of b into equation (1)
a + b = 35
a + 22 = 35
Subtract 22 from both sides of the equation
a = 13.
Therefore, Ralph bought 22 of one type, and 13 of the other type of donut
